Question

select the best description of the following exponential equation.
$f(x)=5(0.95)^{x}$
show your work here
\bigcirc decaying by 95\\% with every unit of $x$.
\bigcirc growing by 95\\% with every unit of $x$.
\bigcirc decaying by 5\\% with every unit of $x$.
\bigcirc growing by 5\\% with every unit of $x$.

Explanation:

Step1: Identify decay/growth form

The general exponential form is $f(x) = a(b)^x$, where $b$ is the growth/decay factor.

Step2: Analyze the base value

Here, $b = 0.95$, which is less than 1, so it is decay.

Step3: Calculate decay rate

Decay rate = $1 - b = 1 - 0.95 = 0.05 = 5\%$.

Answer:

Decaying by 5% with every unit of $x$.