Question

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

Explanation:

Step1: Recall exponential function form

The standard exponential function is $f(x)=a(b)^x$, where $a
eq0$, $b>0,b
eq1$.

Step2: Test point $(2,80)$ in first option

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

Step3: Verify other options (elimination)

For $f(x)=5(x)^4$: $f(2)=5(2)^4=5\times16=80$, but this is a polynomial, not exponential.
For $f(x)=4(5)^x$: $f(2)=4(5)^2=4\times25=100
eq80$.
For $f(x)=4(x)^5$: $f(2)=4(2)^5=4\times32=128
eq80$, and this is a polynomial.

Answer:

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