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

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = a(b)^x$. We need to check each option by substituting $x = 2$ and $y=36$.

Step2: Check option 1

For $f(x)=4(3)^x$, when $x = 2$, $f(2)=4\times(3)^2=4\times9 = 36$.

Step3: Check option 2

For $f(x)=4(x)^3$, when $x = 2$, $f(2)=4\times(2)^3=4\times8 = 32\neq36$.

Step4: Check option 3

For $f(x)=6(3)^x$, when $x = 2$, $f(2)=6\times(3)^2=6\times9 = 54\neq36$.

Step5: Check option 4

For $f(x)=6(x)^3$, when $x = 2$, $f(2)=6\times(2)^3=6\times8 = 48\neq36$.

Answer:

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