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) = (35 t^2 + 125t + 200)/(t^2 + 6 t + 40)

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

Answer 1

The population (in thousands) at year t is given by

P(t) = (35 t^2 + 125t + 200)/(t^2 + 6 t + 40)
where t is the number of years from the current year, or current year means t=0.

So calculate P(0) by putting t=0 on the right hand side of the equation to get
P(0) = (35 (0)^2 + 125(0) + 200)/((0)^2 + 6 (0) + 40)

I get P(0) = 5 (means population=5000)

Answer 2

To find the current population of Glen Cove, we need to evaluate the function P(t) at t = 0.

The formula for the current population, P(0), is:

P(0) = (35 (0)^2 + 125(0) + 200)/((0)^2 + 6(0) + 40)

Simplifying this expression, we have:

P(0) = 200/40 = 5

Therefore, the current population of Glen Cove is 5 thousand (5,000).