Question

select the best description of the following exponential equation.$f(x)=87(0.52)^x$show your work herehint: to add an exponent ($x^a$), type \exponent\ or press \^\$\bigcirc$ growing by 52% with every unit of $x$.$\bigcirc$ decaying by 52% with every unit of $x$.$\bigcirc$ growing by 48% with every unit of $x$.$\bigcirc$ decaying by 48% 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 rate of growth/decay. If $0<1+r<1$, it is decay.

Step2: Identify the base value

Here, $1+r = 0.52$. Solve for $r$:
$r = 0.52 - 1 = -0.48$

Step3: Interpret the rate

A negative $r$ means decay. The magnitude $0.48$ is 48%, so it decays by 48%.

Answer:

Decaying by 48% with every unit of $x$