How can I build power function through point?

Please, help me! I have the coordinates of the curve y = [150 150 130 130 130 100 100 100 80 80 80 60], x = [52000 70000 74000 96000 100000 170000 220000 245000 530000 720000 810000 4900000]. This curve well described by power function. How can I build the same curve passing through the point A(68856, 210) and get it equation?

[Jan]

This sounds like a homework question. If this is the case, please post what you have tried so far and ask a specific question concerning your code. By the way, these are your data:

[Irene Dzhavadova]

Sorry I messed up x and y. I tried to approximate this graph in Curve Fitting Toolbox and there I found equation of it. Please help me raise this curve so that it passes through point A and get its equation.

[Jan]

The screenshot is hard to read due to scaling.

[Torsten]

As model to fit, use

y = a*(x^b-210^b) + 68856

[Irene Dzhavadova]

Torsten, thank you very much for the answer!

But I have an additional question. If I will have not only point A, but several points, how can I approximate these several points and a raised curve?

[Torsten]

If points are added, you will have to fit your model again. As a result, you'll get different values for a, b and c.

Answer 1

[Sayyed Ahmad]

I would do something like this:

 x = [52000 70000 74000 96000 100000 170000 220000 245000 530000 720000 810000 4900000];
 y = [150 150 130 130 130 100 100 100 80 80 80 60];
 p=polyfit(log(x),sqrt(y),2)
 x1=linspace(min(x),max(x),100);
 y1=polyval(p,log(x1)).^2;
 plot(x,y,'r*',x1,y1,'b-')

I hope that is waht you looking for.

[Irene Dzhavadova]

Sayyed Ahmad, many thanks! This is exactly how I want. But You solved part of the problem. Maybe you know how to raise this curve so it will pass through point A (68856, 210)? And if I will have not only a point A but a few points, how to approximate this points and raised curve?

[Sayyed Ahmad]

you can shift it.

y(a)-(y1)=dy

y=f(x)+dy

but you could be only met one point. But If you do that, the deviation will increase. I don't want to recomend you this way.

I don't know what is the aim of this calculation. I will try to reduce the standard diviation with changing in the value n in polyfit.

p=polyfit(x,y,n)

n could be 1, 2, 3, 4, 5 and so on.

Try to change them to find out your acceptable p.

x = [52000 70000 74000 96000 100000 170000 220000 245000 530000 720000 810000 4900000];
 y = [150 150 130 130 130 100 100 100 80 80 80 60];
 for i=1:5
 p=polyfit(log(x),sqrt(y),i)
 x1=linspace(min(x),max(x),100);
 y1=polyval(p,log(x1)).^2;
 plot(x,y,'r*',x1,y1,'-')
 hold on
 end

[Irene Dzhavadova]

Sayyed Ahmad, thanks! I'll try this.