Question

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

Explanation:

Step1: Recall growth function form

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

Step2: Analyze each option

• $f(x)=0.25(5.25)^x$: $a=0.25>0$, $b=5.25>1$
• $f(x)=6(0.25)^x$: $b=0.25<1$ (decay)
• $f(x)=(-1.25)^x$: $a=-1.25<0$, $b$ negative (not valid growth)
• $f(x)=-4.25^x$: $a=-1<0$ (not valid growth)

Answer:

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