Question

which equation represents an exponential function that passes through the point (2, 36)?
$f(x) = 6(x)^3$
$f(x) = 6(3)^x$
$f(x) = 4(x)^3$
$f(x) = 4(3)^x$

Explanation:

Step1: Recall exponential function form

An exponential function has the form $f(x) = a(b)^x$, where $a
eq0$, $b>0$, $b
eq1$. This eliminates options with $x$ as the base (polynomial functions: $f(x)=6(x)^3$ and $f(x)=4(x)^3$).

Step2: Test remaining options with $(2,36)$

First test $f(x)=6(3)^x$:
Substitute $x=2$:
$f(2) = 6(3)^2 = 6\times9 = 54
eq 36$
Next test $f(x)=4(3)^x$:
Substitute $x=2$:
$f(2) = 4(3)^2 = 4\times9 = 36$
This matches the given point.

Answer:

$f(x) = 4(3)^x$