Please and thank you! 13) The market research department for an automobile company estimates thatsales (in millions of dollars) of a new electric car will increase at the monthly rateof S'(t) = 4e0:084total sales during the first 6 months after the introduction of the car?t months after the introduction of the car. What are the estimated

Name: Please and thank you! 13) The market research department for an automo
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please and thank you! 13) The market research department for an automobile company estimates thatsales (in millions of dollars) of a new electric car will increase at the monthly rateof S'(t) = 4e0:084total sales during the first 6 months after the i

Given data: The expression for the rate at which electric car increases is S'(t)=4e-0.08t. The given tie is t=6 months. Integrate the given expression with respect to time. ∫S'tdt=∫4e-0.08tdtS(t)=4-0.08e-0.08t+C=-50e-0.08t+C..............(I) Initially at t=0, the sales are also zero, substitute 0 for t and 0 for S(t) in the above expression. 0=-50e-0.080+C0=-50+CC=50Substitute 50 for C in the equation(I). St=-50e-0.08t+50=501-e-0.08t Substitute 6 for t in the above expression. S6=501-e-0.086=501-e-0.48=$19.06 million Thus, the total sales during the first six months after the car introduction are $19.06 million.