A major corporation is building a 4325 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 Clove's population (in thousands) t yr from now will be given by the following function

Question

A major corporation is building a 4325 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 Clove's population (in thousands) t yr from now will be given by the following function

P(t) = (45 t^2 + 125t + 300)/(t^2 + 4 t + 150)

(a) What is the current population of Glen Cove?
people

(b) What will be the population in the long run?
people

Answer 1

t=0, so P(0) = 300/150 = 2, or 2,000

as t grows large, P(t) =~ 45t^2/t^2 = 45, so P will approach 45,000