The sales of a new high-tech item (in thousands) are given by S(t) = 93- 110e -0

Question

The sales of a new high-tech item (in thousands) are given by S(t) = 93- 110e -04t where t represents time in years. Find the rate of change of sales at each time. After 1 year, After 5 years, What is happening to the rate of change of sales as time, The rate of change after 1 year is (Round to three decimal places as needed.) The rate of change after 5 years is (Round to three decimal places as needed.) What is happening to the rate of change of sales as time goes on? First it decreases, then it increases. First it increases, then it decreases. It always decreases. It always increases. Does the rate of change of sales ever equal zero? No Yes

Explanation / Answer

Given, S(t) = 93 - 110e-0.4t

Rate of change of sales is :

S'(t) = 44e-0.4t

(a) At t = 1 year, S'(t) = 44e-0.4 = 29.494

(b) At t =5 years, S ' (t) = 44e-2 = 5.955

(c) As clearly observed, S'(t) is a exponentially decreasin function i.e. it keeps on decreasing as time progresses. It always decreases

(d) Theoretically, S'(t) = 0 only when infinite time has passed. But for practical situations, we cannot wait for infinite tine. Therefore, NO, the rate of sales never becomes zero

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