Question

select the best description of the following exponential equation.
$f(x)=88(4.34)^x$
show your work here

• growing by 434% with every unit of $x$
• decaying by 334% with every unit of $x$
• decaying by 434% with every unit of $x$
• growing by 334% 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, and $1+r>1$.

Step2: Match given function to form

Given $f(x)=88(4.34)^x$, so $1+r=4.34$.

Step3: Calculate growth rate

Solve for $r$: $r = 4.34 - 1 = 3.34$. Convert to percentage: $3.34\times100\%=334\%$.

Step4: Confirm growth type

Since $4.34>1$, this is exponential growth.

Answer:

Growing by 334% with every unit of $x$