Question

select the best description of the following exponential equation.$f(x)=68(0.88)^x$show your work here$\bigcirc$ growing by 88% with every unit of $x$.$\bigcirc$ decaying by 88% with every unit of $x$.$\bigcirc$ decaying by 12% with every unit of $x$.$\bigcirc$ growing by 12% with every unit of $x$.

Explanation:

Step1: Recall exponential form

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

Step2: Compare to given function

Given $f(x)=68(0.88)^x$, so $1+r=0.88$. Solve for $r$:
$r = 0.88 - 1 = -0.12$

Step3: Interpret the rate

A negative $r$ means decay. The magnitude $0.12$ is 12%, so it decays by 12% per $x$ unit.

Answer:

Decaying by 12% with every unit of $x$