Question

The population of a town is 6,000 and is increasing at a rate of 3% each year.

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

[AI-generated answer — Bot GPT 3.5]

To find the population of the town after 5 years, we can use the exponential function

P(t) = P₀ * (1 + r)^t

where P(t) is the population after t years, P₀ is the initial population, r is the growth rate as a decimal, and t is the number of years.

In this case, P₀ = 6,000, r = 0.03, and t = 5.

Plugging in these values, we get:

P(5) = 6,000 * (1 + 0.03)^5

P(5) = 6,000 * (1.03)^5

P(5) = 6,000 * 1.159274... (rounded to 6 decimal places)

P(5) = 6,955.645... (rounded to 6 decimal places)

Rounded to the nearest whole number, the population of the town after 5 years is 6,956.