Question

Use the exponential function you wrote for problem 5 to find the population of the town after 5 years. Show your work and round your answer to the nearest whole number.

Answer 1

To find the population of the town after 5 years, we plug in t = 5 into the exponential function we wrote for problem 5.

P(t) = 1000 * (1 + 0.07/12)^(12 * t)

P(5) = 1000 * (1 + 0.07/12)^(12 * 5)

Simplifying inside the parentheses:

P(5) = 1000 * (1 + 0.00583)^(60)

Calculating the exponential term:

P(5) = 1000 * (1.00583)^(60)

Using a calculator, we find:

P(5) ≈ 1000 * 1.352208

P(5) ≈ 1352.208

Since we need to round to the nearest whole number, the population of the town after 5 years is approximately 1352.