Question

select the best description of the following exponential equation.
$f(x) = 38(1.82)^x$
show your work here
hint: to add an exponent ($x^n$), type \exponent\ or press \^\
\bigcirc decaying by 82\\% with every unit of $x$.
\bigcirc growing by 182\\% with every unit of $x$.
\bigcirc growing by 82\\% with every unit of $x$.
\bigcirc decaying by 182\\% with every unit of $x$.

Explanation:

Step1: Recall exponential function form

The standard exponential function is $f(x) = a(b)^x$, where $a$ is the initial value, and $b$ is the growth/decay factor.

Step2: Identify growth/decay type

Since $b=1.82 > 1$, this is exponential growth.

Step3: Calculate growth rate

Growth rate = $(b - 1) \times 100\%$.
$(1.82 - 1) \times 100\% = 0.82 \times 100\% = 82\%$

Answer:

Growing by 82% with every unit of $x$.