Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

$y = 15(0.94)^x$

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = a(b)^x$, where $a$ is the initial value and $b$ is the base. If $b>1$, it is growth; if $0 < b<1$, it is decay.
Here, $b = 0.94$ and $0<0.94<1$, so it is decay.

Step2: Calculate the percentage rate of decrease

The rate of decrease $r$ is related to $b$ by the formula $b=1 - r$.
We know $b = 0.94$, so $0.94=1 - r$.
Solving for $r$, we get $r=1 - 0.94=0.06$.
To convert $r$ to a percentage, we multiply by 100. So the percentage rate of decrease is $r\times100 = 6\%$.

Answer:

The function represents decay and the percentage rate of decrease is $6\%$.