Question

select the best description of the following exponential equation.
$f(x)=93(2.05)^x$
show your work here
$circ$ growing by 105% with every unit of $x$
$circ$ decaying by 205% with every unit of $x$
$circ$ decaying by 105% with every unit of $x$
$circ$ growing by 205% with every unit of $x$

Explanation:

Step1: Recall exponential growth form

The standard exponential growth formula is $f(x) = a(1+r)^x$, where $a$ is the initial value, $r$ is the growth rate.

Step2: Match given equation to form

Given $f(x)=93(2.05)^x$, set $1+r=2.05$.

Step3: Calculate growth rate $r$

$r=2.05-1=1.05$, convert to percentage: $1.05\times100\%=105\%$.

Step4: Identify growth/decay

Since $1+r>1$, this is exponential growth.

Answer:

Growing by 105% with every unit of $x$