Question

Determine whether the function below is exponential growth or exponential decay, and find the percentage rate of change. P(t)=8.5 (0.92)t

answer choices:


A
Exponential decay; 8.5%

B
Exponential decay; 8%

C
Exponential growth; 8%

D
Exponential growth; 8.5%

Answer 1

To determine whether the function \( P(t) = 8.5(0.92)^t \) represents exponential growth or decay, we can look at the base of the exponent, which is 0.92.

- If the base is greater than 1, the function represents **exponential growth**.
- If the base is between 0 and 1 (as it is here with 0.92), the function represents **exponential decay**.

Since 0.92 is less than 1, this function represents **exponential decay**.

Next, we need to find the percentage rate of change. The formula for the percentage rate of change in an exponential decay function is given by:

\[
\text{Rate of change} = (1 - \text{base}) \times 100
\]

In this case:

\[
\text{Rate of change} = (1 - 0.92) \times 100 = 0.08 \times 100 = 8\%
\]

So, the function represents **exponential decay** with a percentage rate of change of **8%**.

Therefore, the correct answer is:

**B Exponential decay; 8%**