posted by Ellen on .
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?
(c) Find the rate of growth of the demand after the tenth month.
computers per month
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))
= 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