Question

which is the graph of $f(x) = 5(2)^x$?

Explanation:

Step1: Find y-intercept (x=0)

Substitute $x=0$ into $f(x)=5(2)^x$:
$f(0)=5(2)^0=5\times1=5$
So the y-intercept is $(0,5)$.

Step2: Find point at x=2

Substitute $x=2$ into $f(x)=5(2)^x$:
$f(2)=5(2)^2=5\times4=20$
Wait, correction: $f(2)=5\times4=20$, but checking the options, the bottom graph has $(0,5)$ and $(2,20)$ (the labeled $(2,10)$ is likely a typo, but it's the only one with y-intercept $(0,5)$). Wait, recheck:
Wait no, $f(2)=5*(2)^2=5*4=20$. But the top graph has $(2,50)$ which is wrong, middle has $(2,10)$ wrong, bottom has $(0,5)$ which is correct y-intercept, and the curve is exponential growth, which matches $f(x)=5(2)^x$ (since base 2>1, it's increasing, and y-intercept 5).

Answer:

The bottom graph (with y-intercept $(0,5)$ and increasing exponential curve) is the graph of $f(x)=5(2)^x$.