Question

question a town has a population of 5000 and grows at 3.5% every year. what will be the population after 15 years, to the nearest whole number? answer attempt 2 out of 2 8578 submit answer

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is $P(t) = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the growth rate (in decimal), and $t$ is the time in years.

Step2: Convert the growth rate to decimal

The growth rate is 3.5%, so $r = \frac{3.5}{100} = 0.035$.

Step3: Substitute the values into the formula

We have $P_0 = 5000$, $r = 0.035$, and $t = 15$. So, $P(15) = 5000(1 + 0.035)^{15}$.

Step4: Calculate the value

First, calculate $(1 + 0.035)^{15} \approx 1.035^{15} \approx 1.706868$. Then, multiply by 5000: $5000 \times 1.706868 \approx 8534.34$. Rounding to the nearest whole number gives 8534.

Answer:

8534