Question

3. Kingman’s population at the end of 2017 was 29,472, and its growth rate has been 1.42% each year. Jeff lives in Kingman and wants to track the predicted population growth over time for an experiment. a. Write an equation to model the population growth of Kingman. b. What was the population in June of 2018? Round your answer to the nearest integer. c. What will the population be at the end of 2018? Round your answer to the nearest integer. d. What will the population be in 2025? Round your answer to the nearest integer

Answer 1

Answers:

(a) the population function is exponential in the number of years (t) after 2017:

`N(t) = 29472\cdot 1.0142^t`

(b) Although the model is defined on a yearly basis, we can answer the question by calculating the projected population at the end of 2018 (t=1) and, under the assumption of same birth rate every month, take half of the yearly increase (end of June):

N(1) = 29890.50

June population:
`N(0) + (N(1)-N(0))/(2)\approx29472+209=29681`

(c) N(1) = 29891 (see (b) above)

(d) Population in 2025 is the function value at t=2025-2017=8

`N(8) = 29472\cdot 1.0142^8=32991.22...\approx 32991`