The sales of a new high-tech item (in thousands) are given by S(t) 100 e 0.4t wh

Question

The sales of a new high-tech item (in thousands) are given by S(t) 100 e 0.4t where t represents time in years. Find the rate of change of sales at each time. a.) After 1 year. b.) After 5 years. c.) What is happening to the rate of change of sales as time goes on? d.) Does the rate of change of sales ever equal zero? a. The rate of change after 1 year is (Round to three decimal places as needed.) b. The rate of change after 5 years is L (Round to three decimal places as needed.) c. What is happening to the rate of change of sales as time goes on? A. First it decreases then it increases OB. It always increases OC. First it increases, then it decreases OD. t always decreases d. Does the rate of change of sales ever equal zero? O No O Yes

Explanation / Answer

ds/dt = 40e^(-0.4t)

a) so , rate of change after 1 year = 40e^(-0.4*1) = 26.813

b) so , rate of change after 1 year = 40e^(-0.4*5) = 5.413

c) The rate always decreases with time

d) No it will never become zero

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