{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":61057,"title":"Radioactive Decay Chain","description":"A radioactive decay chain consists of a series of nuclides, each decaying into the next.\r\nSuppose we have a chain of N isotopes:\r\n         \r\nEach isotope decays exponentially based on its decay constant ()\r\nGiven:\r\nA vector of decay constants lambda = []\r\nAn initial vector of isotope amounts A0 = []\r\nA scalar time t\r\nCompute the amounts of all isotopes at time t. Round to the nearest integer. All decay constants will be in inverse seconds and time will be in seconds.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 277.938px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 138.969px; transform-origin: 408px 138.969px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA radioactive decay chain consists of a series of nuclides, each decaying into the next.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSuppose we have a chain of N isotopes:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.75px; text-align: left; transform-origin: 385px 10.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; 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\" width=\"167\" height=\"20\" style=\"width: 167px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e      \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach isotope decays exponentially based on its decay constant (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eλ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 64.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 32.2188px; transform-origin: 392px 32.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.5px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.75px; text-align: left; transform-origin: 364px 10.75px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA vector of decay constants \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003elambda = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"93.5\" height=\"20\" style=\"width: 93.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.5px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.75px; text-align: left; transform-origin: 364px 10.75px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn initial vector of isotope amounts \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eA0 = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"125.5\" height=\"20\" style=\"width: 125.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.7188px; text-align: left; transform-origin: 364px 10.7188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA scalar time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the amounts of all isotopes at time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Round to the nearest integer. All decay constants will be in inverse seconds and time will be in seconds.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = decayChain(lambda, A0, t)\r\n  y = exp(1)^(-lambda*t);\r\nend","test_suite":"%%\r\nlambda=[.88865,2.056817,0.029002,0.0011216,1.2529e-7,2.2938e-7];\r\nA0=[1e9,0,0,0,0,0,0];\r\nassert(isequal(decayChain(lambda,A0,10000), [ 0           0           0       14024   998849955     1134828        1193]));\r\nassert(isequal([138243      105163   784303256   214380309     1073029           0           0],decayChain(lambda,A0,10)));\r\nassert(isequal(decayChain(lambda,A0,100), [0           0    57681501   871543063    70775085         350           0]));\r\nassert(isequal(decayChain(lambda,A0,1000), [0           0           0   339476435   660476584       46977           4]));\r\nassert(isequal(decayChain(lambda,A0,1e5), [0           0           0           0   987663955    12196633      139412]));\r\nassert(isequal(decayChain(lambda,A0,1e6), [0           0           0           0   882343569   104897417    12759014]));\r\nassert(isequal(decayChain(lambda,A0,1e8), [ 0           0           0           0        3621        4358   999992022]));\r\nassert(isequal(decayChain(lambda,A0,1.5e8), [ 0           0           0           0           7           8   999999985]));\r\n%%\r\nrng(2718);\r\nD=decayChain(rand(1,10),randi(1e9,1,11),1000);\r\nassert(isequal(D(4),24561750));\r\nassert(isequal(D(8),600336));\r\nassert(isequal(D(11),6050220432));\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":145982,"edited_at":"2025-11-02T03:59:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-02T03:58:41.000Z","updated_at":"2026-02-26T13:20:07.000Z","published_at":"2025-11-02T03:58:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA radioactive decay chain consists of a series of nuclides, each decaying into the next.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose we have a chain of N isotopes:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_1\\\\longrightarrow A_2\\\\longrightarrow A_3 ... \\\\longrightarrow A_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e      \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach isotope decays exponentially based on its decay constant (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lambda\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA vector of decay constants \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elambda = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lambda_1, \\\\lambda_2, \\\\lambda_3, ... \\\\lambda_{n-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn initial vector of isotope amounts \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA0 = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA1_0, A2_0, A3_0, ... An_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA scalar time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the amounts of all isotopes at time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Round to the nearest integer. All decay constants will be in inverse seconds and time will be in seconds.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":61057,"title":"Radioactive Decay Chain","description":"A radioactive decay chain consists of a series of nuclides, each decaying into the next.\r\nSuppose we have a chain of N isotopes:\r\n         \r\nEach isotope decays exponentially based on its decay constant ()\r\nGiven:\r\nA vector of decay constants lambda = []\r\nAn initial vector of isotope amounts A0 = []\r\nA scalar time t\r\nCompute the amounts of all isotopes at time t. Round to the nearest integer. All decay constants will be in inverse seconds and time will be in seconds.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 277.938px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 138.969px; transform-origin: 408px 138.969px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA radioactive decay chain consists of a series of nuclides, each decaying into the next.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSuppose we have a chain of N isotopes:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.75px; text-align: left; transform-origin: 385px 10.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"167\" height=\"20\" style=\"width: 167px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e      \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach isotope decays exponentially based on its decay constant (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eλ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 64.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 32.2188px; transform-origin: 392px 32.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.5px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.75px; text-align: left; transform-origin: 364px 10.75px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA vector of decay constants \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003elambda = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"93.5\" height=\"20\" style=\"width: 93.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.5px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.75px; text-align: left; transform-origin: 364px 10.75px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn initial vector of isotope amounts \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eA0 = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"125.5\" height=\"20\" style=\"width: 125.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.7188px; text-align: left; transform-origin: 364px 10.7188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA scalar time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the amounts of all isotopes at time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Round to the nearest integer. All decay constants will be in inverse seconds and time will be in seconds.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = decayChain(lambda, A0, t)\r\n  y = exp(1)^(-lambda*t);\r\nend","test_suite":"%%\r\nlambda=[.88865,2.056817,0.029002,0.0011216,1.2529e-7,2.2938e-7];\r\nA0=[1e9,0,0,0,0,0,0];\r\nassert(isequal(decayChain(lambda,A0,10000), [ 0           0           0       14024   998849955     1134828        1193]));\r\nassert(isequal([138243      105163   784303256   214380309     1073029           0           0],decayChain(lambda,A0,10)));\r\nassert(isequal(decayChain(lambda,A0,100), [0           0    57681501   871543063    70775085         350           0]));\r\nassert(isequal(decayChain(lambda,A0,1000), [0           0           0   339476435   660476584       46977           4]));\r\nassert(isequal(decayChain(lambda,A0,1e5), [0           0           0           0   987663955    12196633      139412]));\r\nassert(isequal(decayChain(lambda,A0,1e6), [0           0           0           0   882343569   104897417    12759014]));\r\nassert(isequal(decayChain(lambda,A0,1e8), [ 0           0           0           0        3621        4358   999992022]));\r\nassert(isequal(decayChain(lambda,A0,1.5e8), [ 0           0           0           0           7           8   999999985]));\r\n%%\r\nrng(2718);\r\nD=decayChain(rand(1,10),randi(1e9,1,11),1000);\r\nassert(isequal(D(4),24561750));\r\nassert(isequal(D(8),600336));\r\nassert(isequal(D(11),6050220432));\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":145982,"edited_at":"2025-11-02T03:59:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-02T03:58:41.000Z","updated_at":"2026-02-26T13:20:07.000Z","published_at":"2025-11-02T03:58:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA radioactive decay chain consists of a series of nuclides, each decaying into the next.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose we have a chain of N isotopes:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_1\\\\longrightarrow A_2\\\\longrightarrow A_3 ... \\\\longrightarrow A_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e      \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach isotope decays exponentially based on its decay constant (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lambda\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA vector of decay constants \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elambda = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lambda_1, \\\\lambda_2, \\\\lambda_3, ... \\\\lambda_{n-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn initial vector of isotope amounts \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA0 = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA1_0, A2_0, A3_0, ... An_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA scalar time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the amounts of all isotopes at time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Round to the nearest integer. All decay constants will be in inverse seconds and time will be in seconds.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"isotopes\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"isotopes\"","current_player":null,"sort":"map(difficulty_value,0,0,999) 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