Question

the lion population in a certain reserve drops by 5% every year. currently, the populations size is 200. write a function that gives the lion population size, p(t), t years from today. p(t) =

Explanation:

Step1: Identify decay factor

Since the population drops by 5% yearly, the remaining proportion is $1 - 0.05 = 0.95$.

Step2: Set up exponential decay function

Use initial population $P_0=200$, decay factor $0.95$, and time $t$. The general form of exponential decay is $P(t)=P_0 \times (decay\ factor)^t$.
$P(t)=200 \times (0.95)^t$

Answer:

$P(t)=200(0.95)^t$