Answers:
(a) the population function is exponential in the number of years (t) after 2017:
[tex]N(t) = 29472\cdot 1.0142^t[/tex]
(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: [tex]N(0) + \frac{N(1)-N(0)}{2}\approx29472+209=29681[/tex]
(c) N(1) = 29891 (see (b) above)
(d) Population in 2025 is the function value at t=2025-2017=8
[tex]N(8) = 29472\cdot 1.0142^8=32991.22...\approx 32991[/tex]
