PLEASE SHOW ALL OF YOUR WORK!!! THIS MEANS SHOW STEP BY STEP HOW YOU ARRIVED AT

Question

PLEASE SHOW ALL OF YOUR WORK!!! THIS MEANS SHOW STEP BY STEP HOW YOU ARRIVED AT YOUR ANSWER(S). INCLUDE ANY EQUATIONS OR FORMULAS USED TO ARRIVE AT YOUR ANSWER(S). THANKS!

4. A sporting goods store predicts that revenue from the sale of ski jackets this year is reasonably approximated by R(t) = 4.15 + 3.85 cos (Pit/26) for 0 leq t leq 52, where R(t) is revenue (in thousands of dollars) for a week of sales t weeks after January 1. a. What is the rate of change of revenue 10 weeks after the first of the year? Label your response appropriately. b. What is the expected revenue for the week containing April 11th? Label your response appropriately.

Explanation / Answer

R(t) = 4.15 + 3.85 cos(pi/26 t)

rate of change of revenue, dR/dt = -3.85 *26 sin (pi/26) t)

So rate of change of revenue, dR/dt at t=10, dR/dt(10) = -93.57 $ /week

So at t=10 week, Revenue was decresing at the rate of $93.57/week (Ans)

b) Expected revenue for week of april1

No of weeks from jan1 to april1

31+28+31 = 90

So no. of weeks =13

So Expected revenue for t=13

R(13) = 4.15 + 3.85 cos(pi/26 *13) = 4.15 thousand $ (ans)

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