given the following exponential function, identify whether the change represents growth or decay, and…

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.\n$y = 72(0.913)^x$

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.\n$y = 72(0.913)^x$

Answer

Explanation:

Step1: Compare to standard form

The standard exponential form is $y = a(1+r)^x$, where $a$ is the initial value, $r$ is the rate of change. For decay, $0 < 1+r < 1$. Here, $1+r = 0.913$.

Step2: Calculate decay rate

Solve for $r$: $r = 0.913 - 1 = -0.087$. Convert to percentage: $-0.087 \times 100 = -8.7%$. The negative sign indicates decay.

Answer:

This represents exponential decay with an 8.7% rate of decrease.