#51 Demand for DVD players VCA Television found that monthly demand for it\'s ne

Question

#51 Demand for DVD players VCA Television found that monthly demand for it's new line of DVD players t mo after placeing the players on the market is given by D(t)=4000-3000e^-.06t where (t=0) Graph this function and answer the following questions:

I know how to solve for month 1, 12, and 24 but I am wondering part b of this question which is below. Can you explain how you got the answer please?
B. At what level is the demand expected to stabilize?

Explanation / Answer

So you are looking for the asymptote of the function D(t) To find it, you need to plug infinity into the equation for 't' so write lim t->'infinityi 4000-3000e^-0.6t Clearly e^-0.6*infinity will be ridiculously small. As t approaches infinity, e^-0.6t will approach 0. Therefore 3000e^-0.6t will be zero and D(t) as t approaches infinity=4000-0=4000 Hence, Demand for DVDs will stabilize at 4000

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