Plot the function combining an exponential function and a step function

I have a funtion involving exponential functions and one exponent is a step function of x.

The plot I need is y vs x,

y=(e^(2t)-1)*e^(-2.5x) ,

and t is a step function of x

where t=x for x<10

t=10 for x>=10

Please help me to plot such a function in xy space.

syms x ;
t =piecewise(x<10,x,x>=10,10);
y=(exp(2*t)-1)*exp(-2.5*x);
fplot(y)

The curve I got from the code above is clearly not correct. Could anyone tell me what is wrong and how to fix it? Thanks!

Answer 1

[Riccardo Scorretti]

Hi Nick,

Your program seems correct. Perhaps you need to adapt the range over which the graphic is plotted (the default range is [-5 5]). For instance, in the range [0 20] one obtains:

syms x
t = piecewise(x<10, x, x>=10, 10);
y = (exp(2*t)-1) * exp(-2.5*x);         
fplot(y, [0 20], 'LineWidth', 2); % Plot between [0 20]
grid on ; xlabel('x') ; hold on ; drawnow

Let's check it by removing the function t and plotting separately on [0 10] and [10 20]:

y = (exp(2*x)-1) * exp(-2.5*x);         
fplot(y, [0 10], 'Color', 'r');

y = (exp(2*10)-1) * exp(-2.5*x);         
fplot(y, [10 20], 'Color', 'r');

grid on ; xlabel('x');

[Nick]

Thanks Riccardo! This is exactly what I need.

Answer 2

[Sam Chak]

Hi @Nick

Please check the piecewise function if it is what you desire. Then, check the equation and the plot.

subplot(2, 1, 1)
fplot(@(x) min(x,10), [-1 15])
grid on
xlabel('x')
ylabel('t')
title('Function t(x)')

subplot(2, 1, 2)
fplot(@(x) (exp(2*min(x, 10))-1).*exp(-2.5*x), [-1 15])
grid on
xlabel('x')
ylabel('y')
title('Function y(x)')

Result

[Nick]

Thank you Sam! This helps me a lot and now I know how subplot works.

[Sam Chak]

Don't mention it. There are many tricks and tips you can learn along.