Question

he function $f(x) = a \cdot x^r$ satisfies $f(2) = 1$ and $f(32) = 4$. Find $r$.

Answer 1

trying to lose all the text formatting noise, I get

f(x) = a x^r
satisfies f(2) = 1 and f(32) = 4
So divide the two given points, and you have
32^r/2^r = 4
16^r = 16^(1/2)
r = 1/2