Pre-Calc

The game commission introduces 100 deer into newly acquired state game lands. the population N of the herd is modeled by N=(20(5+3t))/1+0.04t t>/=0
where t is the time in years

a. find the population when t=5, t=10, and t=25

b. what is the limiting size of the herd as time increases?

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  1. 12

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  2. you must mean
    N = 20(5+3t)/(1+.04t)

    plug in t = 5
    N = 20(5+15)/(1 + .04(5))
    = 400/1.02
    = 2000
    Do the others likewise.

    as t ---> large
    n = (100 + 60(large))/(1 + .04 large)
    = appr 60large/.04large
    = appr 60/.04 ---> 1500
    the limiting size = 1500

    e.g. let t = 100,000
    N = 20(300005)/(1 + 4000) = 1500.025

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