Question

which equation represents an exponential function that passes through the point (2, 80)?
① $f(x) = 4(x)^2$
② $f(x) = 5(x)^4$
③ $f(x) = 4(5)^x$
④ $f(x) = 5(4)^x$

Explanation:

Step1: Recall exponential function form

An exponential function has the form $f(x)=a(b)^x$, where $a
eq0$, $b>0$, $b
eq1$. First eliminate non-exponential options: $f(x)=4(x)^2$ and $f(x)=5(x)^4$ are polynomial, not exponential.

Step2: Test $f(x)=4(5)^x$ at $x=2$

Substitute $x=2$: $f(2)=4(5)^2=4\times25=100
eq80$

Step3: Test $f(x)=5(4)^x$ at $x=2$

Substitute $x=2$: $f(2)=5(4)^2=5\times16=80$

Answer:

$f(x)=5(4)^x$