For the function $f$, for each increase in the value of $x$ by $c$, w…

Question

Prompt

For the function

f

, for each increase in the value of

x

c

, where

c

is a positive constant, the value of

f (x)

increases by a factor of 27. Which of the following equivalent forms of the function

f

displays

1/ c

as a coefficient of

x

f (x) = 32 (3)^{\frac{1}{2} x}

f (x) = 32 (27)^{\frac{1}{c} x}

f (x) = 32 (9)^{\frac{1}{4} x}

f (x) = 32 (2 7^{\frac{1}{3} x})^{\frac{1}{2}}