Question

which is an exponential growth function?
$f(x) = 6(0.25)^x$
$f(x) = 0.25(5.25)^x$
$f(x) = -4.25^x$
$f(x) = (-1.25)^x$

Explanation:

Step1: Recall exponential growth form

An exponential growth function has the form $f(x)=ab^x$, where $a>0$ and $b>1$.

Step2: Analyze Option 1

For $f(x)=6(0.25)^x$, $b=0.25<1$, so it is decay.

Step3: Analyze Option 2

For $f(x)=0.25(5.25)^x$, $a=0.25>0$ and $b=5.25>1$, fits growth criteria.

Step4: Analyze Option 3

For $f(x)=-4.25^x$, $a=-4<0$, so it does not represent growth.

Step5: Analyze Option 4

For $f(x)=(-1.25)^x$, $b$ is negative, so it is not a valid exponential growth function (output alternates sign, not consistent growth).

Answer:

$f(x) = 0.25(5.25)^x$