(4,3) , (8,15) Write a power function y=ax^b whose graph passes through the given points

We are asked to write the equation for a power function whose graph passes through the points (4,3) and (8,15).
We substitute the known values of x and y into the basic equation to get two equations with two unknowns (a and b) and then solve the system for the coefficients.
3=a*4^b, 15=a*8^b
Solving the first equation for a we get:
a=3/(4^b)
Substitute this expression for a in the second equation to get:
15=3/(4^b)*8^b
15=3*(8/4)^b
2^b=5
So b=(ln(5))/(ln(2))~~2.322
Now substitute for b to get a:
a=3/(4^b)=3/(4^((ln(5))/(ln(2))))=3/25=.12
So the model is y=3/25x^((ln(5))/(ln(2)))"or" y~~.12x^2.322