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Math·Advanced Math·Nonlinear functions

hard

For the function $f$, for every increase of $2$ in the value of $x$, the value of $f(x)$ increases by a factor of $c$, where $c$ is a constant. Which of the following equivalent forms of function $f$ displays the value of $c$ as the base or the coefficient?

A

$f(x)=42(2{)}^{6x}$

B

$f(x)=42(8{)}^{2x}$

C

$f(x)=42(64{)}^x$

D

$f(x)=42(4,096{)}^{\frac{x}{2}}$