Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
( y = 51(0.91)^x )

Explanation:

Step1: Identify growth/decay factor

The general form of an exponential function is $y = a(b)^x$, where $b$ is the growth/decay factor. For $y = 51(0.91)^x$, $b = 0.91$. Since $0 < b < 1$, this is decay.

Step2: Calculate percent decrease

Percent change is found by $|1 - b| \times 100\%$.
$\text{Percent decrease} = |1 - 0.91| \times 100\% = 0.09 \times 100\% = 9\%$

Answer:

Decay, 9% decrease