math

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)=25t^2+125t+200/t^2+2t+100


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

?? people

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

?? people

  1. 👍 0
  2. 👎 0
  3. 👁 1,898
  1. I have an inkling that your equation might be
    p(t) = (25t^2 + 125t + 200)/(t^2 + 2t + 100)

    current ----> t = 0
    p(0) = 200/100 = 2, but it was measured in thousands
    so the current population is 2000

    in the long run ----> x --> ∞

    as x gets bigger, we are left with the dominating terms of 25t^2/t^2 , thus the function approaches 25

    so in the "long run" the population would be 25000

    1. 👍 3
    2. 👎 1

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