how to solve system of two non linear equations? (power law)

I have two equation related to power law equation solution.

1. I have two points, and I want to find the power "b" in power law equation Y = ax^b. the points are x,y = (0.0226336, 24.988) & (0.0180306, 0.179498)
2. I have one point and the power b. point x,y = (0.0226336, 24.988) and power b = 2. Now I want to plot the equation using point and power b.

Answer 1

[Shaik mohammed ghouse basha]

Hello,

As per my understanding of your question, you have an equation of form . In first part with given two points on curve you want to find the variable b. In second part with a point and value of b you want to plot the curve.

Part I:

Given two points on curve as (0.0226336, 24.988) & (0.0180306, 0.179498).

Let points be

As both points satisfy the power law equation we can write:

dividing both these quations you get:

Take log on both sides of this equation you get:

y1 = 24.988;
y2 = 0.179498;
x1 = 0.0226336;
x2 = 0.0180306;

b = log(y1/y2) / log(x1/x2);
disp(b);

   21.7095

Part II:

To plot the equation we need to find the value of a.

As given point satisfy the equation we can use this to find a.

y1 = 24.988;
x1 = 0.0226336;
b = 2;

a = y1/x1.^b;


x = -10:0.01:10; 
%x goes from -10 to 10 with an increment of 0.01

y = a*x.^b;

plot(x, y)

[Faisal]

@Shaik mohammed ghouse basha Thank you Shaik. You solved my problem.