Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
( y = 40(0.97)^x )

Explanation:

Step1: Identify growth/decay factor

The general exponential form is $y = a(b)^x$, where $b$ is the base. Here, $b = 0.97$. Since $0 < b < 1$, this is decay.

Step2: Calculate decay percentage

Subtract the base from 1 to find the rate: $1 - 0.97 = 0.03$. Convert to percentage: $0.03 \times 100 = 3\%$.

Answer:

Decay, 3% decrease