math help

Universal instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by
D(t) = 2900 − 2300e−0.08t (t > 0)
Graph this function and answer the following questions.
(a) What is the demand after 1 month? After 1 year? After 2 years? after 5 years?
after 1 month computers
after 1 year computers
after 2 years computers
after 5 years computers


(b) At what level is the demand expected to stabilize?
computers

(c) Find the rate of growth of the demand after the tenth month.
computers per month

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  1. simply sub in each of the values, I will do the one for 2 years

    at 2 years, t = 24

    D(24) = 2900- 2300e^(-.08(24))
    = 2900-2300e^-1.92
    = appr 2563

    b) notice that as t gets larger, e^-.08t gets smaller.
    So eventually D(t) becomes 2900-0 or 2900

    D'(t) = .08(2300)e^-.08t
    when t = 10
    D'(10) = .08(2300)e^(.08(10)) = 83computers/month

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