Question

1. the population of a town is 2500 and is decreasing at a rate of 3.5% per year. use an exponential function to find the population of the town after 5 years.

Explanation:

Step1: Define decay formula

The exponential decay formula is $P(t) = P_0(1-r)^t$, where $P_0$ is initial population, $r$ is decay rate, $t$ is time.

Step2: Identify given values

$P_0=2500$, $r=0.035$, $t=5$

Step3: Substitute values into formula

$P(5) = 2500(1-0.035)^5 = 2500(0.965)^5$

Step4: Calculate $(0.965)^5$

$0.965^5 \approx 0.8362$

Step5: Compute final population

$2500 \times 0.8362 = 2090.5$

Answer:

Approximately 2091 (rounded to the nearest whole number, since population is a whole count)