Calculus Question

Question

The world population¹ P, in billions, is approximately

P= 7.17e^0.01064t

where t is in years since April 20, 2014. At what rate was the world's population increasing on that date? 

Give your answer in millions of people per year rounded to one decimal place

Answer 1

The rate of increase of the population on April 20, 2014 is the rate of change of the function P at time =0.

dP/dt = (7.17)(.01064)e^(.01064t) or 7.17(.01064) = .07689 billions/year = .07689 x 10^9 people/year or

76.89 x 10^6 people/year or 76.89 million people/year.