Question

The population P of a certain country (in thousands) from 2000 through 2013 can be modeled by P(t) = −14.74t2 + 95.6t + 82,276, 0 ≤ t ≤ 13 where t is the year, with t = 0 corresponding to 2000. (a) According to the model, in what year did the country have its greatest population? (Round your answer to the nearest year.) What was the population? (Round your answer to the nearest whole number.) thousand people (b) According to the model, what will the country's population be in the year 2075? (Round your answer to the nearest whole number.) thousand people

Answer 1

P(t) = -14.74t² + 95.6t + 82,276

(a) P'(t) = -29.48t + 95.6 = 0

t = 3

P(3) = 82,430

(b) P(75) = 6,534