Question

The population of a town is 5655 in 2023. The population grows continuously at a rate of 1.6% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2022. (b) Estimate the population of the town in 2033. Round to the nearest whole person. Show your work.

Answer 1

The exponential growth model used to estimate the future population given a continuous growth rate is P(t) = P0e^rt.

Applying this to the given data, the population of the town in 2033 is estimated to be approximately 6434 people.

Step-by-step explanation:

To determine the population of a town in the future based on a continuous growth rate, we use the exponential growth model.

The exponential growth model is represented by the equation P(t) = P0ert, where P(t) is the population at time t, P0 is the initial population, r is the rate of growth, and e is the base of the natural logarithm (approximately 2.71828).

(a) Given the initial population P0 of 5655 in the year 2023 and a growth rate r of 1.6%, the equation that estimates the population t years after 2022 would be: P(t) = 5655e0.016t

(b) To estimate the population in 2033, which is t = 2033 - 2022 = 11 years after 2022, we substitute t with 11 in the equation: P(11) = 5655e0.016(11)

After calculating the above expression, we get P(11) ≈ 6434.36. Rounding to the nearest whole person gives us an estimated population of 6434 in 2033.