Question

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

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: $f(x)=4(x)^5$ and $f(x)=5(x)^4$ are polynomial functions, not exponential.

Step2: Test remaining option 1: $f(x)=4(5)^x$

Substitute $x=2$ into the function:
$f(2)=4(5)^2=4\times25=100$
This does not equal 80, so this is not the correct function.

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

Substitute $x=2$ into the function:
$f(2)=5(4)^2=5\times16=80$
This matches the given point $(2,80)$.

Answer:

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