Final answer:
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.