pre-Calculus Problem

Question

Write as a power function: y varies directly with the cube root of x and y is 10 when x is 125.

Answer 1

A general power function equation would be:

Since this problem is stating y varies directly as the "cube root" of x, then n = 1/3

So if y = kx^1/3

we can plug in x = 125 and y = 10 to solve for "k"

10 = k(125^1/3)

10 = k(5)

k = 2

Therefore the power function is:

y = 2x^1/3 or y = 2(³√x)