A major corporation is building a 2250 acre complex of homes

A major corporation is building a 2250\"-\" acre complex of homes, offices, stores, schools, and churches in the rural community of Glendale. As a result of this development, the planners have estimated that Glendale’s population (in thousands) t years from now will be given byP(t)=5t^2+125t+400/0.2t^2+10t+50

a. What is the current population of Glendale?

b. What will be the population in the long run?

Solution

Glendale’s population (in thousands) t years from now will be given by

P(t)= (5t^2+125t+400)/(0.2t^2+10t+50)

a) Current population can be found by plugging t=0

P(t=0) = 400/50 = 8 thousand

b) Population as t approaches infinity only l highest terms would be significant

P(t) = 5t^2/0.2t^2 = 10 thousand