Question

the population of a town is 20,000. $p = 20,000(1 - 0.009)^t$ represents the change in population each year. by what percentage does the population decrease each year? options: 0.009%, 1%, 9%, 0.9%

Explanation:

Step1: Recall decay formula form

The standard exponential decay formula is $P = P_0(1 - r)^t$, where $r$ is the annual decay percentage.

Step2: Match given formula to standard

Given $P = 20,000(1 - 0.09)^t$, compare to $P = P_0(1 - r)^t$. Here, $r = 0.09$.

Step3: Convert decimal to percentage

$r = 0.09 = 9\%$

Answer:

9%