Question

question given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. $y = 910(0.94)^{x}$

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 a growth function; if $0 < b<1$, it is a decay function. Here, $a = 910$ and $b = 0.94$. Since $0<0.94<1$, it is a decay function.

Step2: Calculate the percentage rate of decrease

The formula to find the percentage rate of decrease $r$ from the base $b$ of an exponential - decay function is $b=1 - r$. 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 $r = 6\%$.

Answer:

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