Find a power function throught the points (3,5103) and (2,448).

Question

I need help figuring out how to solve this problem.

Answer 1

Let y=ax^b be the function where a and b are constants.

Plug in (3,5103): 5103=a3^b and plug in (2,448): 448=a2^b.

Divide these two equations: 5103/448=(3/2)^b. Take logs: blog(1.5)=log(5103/448).

5103/448=729/64=3^6/2*6=(3/2)^6

So b=6log(3/2)/log(3/2)=6.

Substitute b=6 in y=ax^b=ax^6; so 448=64a and a=448/64=7.

Therefore the function f(x)=7x^6.