Population Growth A major corporation is building a 4,325-acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Cove's population (in thousands) t years from now will be given by
P(t) = (30t^2 + 120t + 120) / (t^2 + 4t + 16).
(a) Find the rate (in thousands of people/year) at which Glen Cove's population is changing with respect to time.
P'(t) = (720t + 1440) / (t^2 + 4t + 16)^2
(b) What will the population be after 10 years? (Round your answer to the nearest person.)
28000 people
At what rate (in people/year) will the population be increasing when t = 10? (Round your answer to the nearest integer.)
4000 people/year
