Math Help - finding values from power functions

1. finding values from power functions

I need help on this math problem. I keep getting the wrong answers for the values for n and a.

Given a power function of the form f(x)=axn , with f(3)=18 and f(6)=72, find n and a .

2. Originally Posted by jojoferni244
I need help on this math problem. I keep getting the wrong answers for the values for n and a.

Given a power function of the form f(x)=axn , with f(3)=18 and f(6)=72, find n and a .
From $18=a\cdot 3^n$ you get $3^n=\dfrac{18}{a}$

Re-write

$72 = a\cdot 6^n~\implies~72=a\cdot 2^n \cdot 3^n$

Now substitute the term of $3^n$ in the 2nd equation:

$72=a\cdot 2^n \cdot \dfrac{18}{a}~\implies~2^n=4~\implies~n=2$

Plug in this value into one of the given equations and solve for a. You'll get $a = 2$

A shortcut:

$72 = a\cdot 6^n$
$18=a\cdot 3^n$

Divide both equations columnwise:

$\dfrac{72}{18}=\dfrac{6^n}{3^n} = 2^n~\implies~ n=2$