Question

station 1: a town’s population is increasing by 2% each year. the population in the year 2000 is 5250 people.
question a: write the model for this scenario.
question b: what would be the population in the year 2020?

Explanation:

Step1: Define exponential growth model

The general annual exponential growth model is $P(t) = P_0(1+r)^t$, where $P_0=5250$, $r=0.02$, and $t$ is years after 2000.

Step2: Build scenario model

$P(t) = 5250(1+0.02)^t = 5250(1.02)^t$

Step3: Calculate $t$ for 2020

$t=2020-2000=20$

Step4: Compute 2020 population

$P(20) = 5250(1.02)^{20}$
First calculate $1.02^{20}\approx1.485947$
Then $5250\times1.485947\approx7801$

Answer:

Question A: $P(t) = 5250(1.02)^t$, where $t$ is years after 2000
Question B: $\approx7801$ people