Question

select the best description of the following exponential equation.
$f(x)=80(5.7)^x$
show your work here
○ growing by 570% with every unit of $x$.
○ growing by 470% with every unit of $x$.
○ decaying by 470% with every unit of $x$
○ decaying by 570% with every unit of $x$.

Explanation:

Step1: Recall exponential growth form

The standard exponential growth/decay form is $f(x)=a(1+r)^x$, where $a$ is the initial value, $r$ is the growth/decay rate. If $1+r>1$, it is growth; if $0<1+r<1$, it is decay.

Step2: Match given equation to form

Given $f(x)=80(5.7)^x$, so $1+r=5.7$. Solve for $r$:
$r=5.7-1=4.7$

Step3: Convert rate to percentage

$4.7 \times 100\% = 470\%$. Since $r>0$, this is growth.

Answer:

Growing by 470% with every unit of $x$.