a. What is the current population of Glen Road b. What will be the population in the long run?

Question

A major corporation is building a 4325-acre complex of homes, offices,stores, schools, and churches in the rural community of Glen Road. As a result of this development, the planners have estimated that Glen Road's population (in thousands) t years now will be given.

 

P(t) 25t^2+125t+200/t^2+5t+40

 

1. What is the current population of Glen Road?

 

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

 

 

Answer 1

P(t) = (25t^2 + 125t + 200)/(t^2 + 5t + 40)

 

P(0) = (25(0)^2 + 125(0) + 200)/((0)^2 + 5(0) + 40)

 

P(0) =200/40 = 20/4 = 5 thousand

 

as t → ∞,

P(t) = (25 + 125/t + 200/t^2)/(1 + 5/t + 40/t^2)

→ (25+0+0)/(1+0+0) = 25 thousand.

Answer 2

Saralee,

 

      The current population is P(0)=200/40=50 thousand

In the long run P(t) ≅25t² as t→∞

 

Jim