Metro Department Store found that t weeks after the end of a sales promotion the volume of sales was given by S(t) = B + Ae-kt (0 sts 4) where B = 49,000 and is equal to the average weekly volume of sales before the promotion. The sales volumes at the end of the first and third weeks were $80,660 and $65,210, respectively. Assume that the sales volume is decreasing exponentially. (a) Find the decay constant k. (Round your answer to five decimal places.) k = (b) Find the sales volume at the end of the fourth week. (Round your answer to the nearest whole number.) Evaluate the definite integral. *64 dx

Metro Department Store found that t weeks after the end of a sales promotion the volume of sales was given by S(t) = B + Ae-kt (0 sts 4) where B = 49,000 and is equal to the average weekly volume of sales before the promotion. The sales volumes at the end of the first and third weeks were $80,660 and $65,210, respectively. Assume that the sales volume is decreasing exponentially. (a) Find the decay constant k. (Round your answer to five decimal places.) k = (b) Find the sales volume at the end of the fourth week. (Round your answer to the nearest whole number.) Evaluate the definite integral. *64 dx

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Metro Department Store found that t weeks after the end of a sales promotion the volume of sales was given by
S(t) = B + Ae-kt
(0 sts 4)
where B = 49,000 and is equal to the average weekly volume of sales before the promotion. The sales volumes at the end of the first and third weeks were $80,660
and $65,210, respectively. Assume that the sales volume is decreasing exponentially.
(a) Find the decay constant k. (Round your answer to five decimal places.)
k =
(b) Find the sales volume at the end of the fourth week. (Round your answer to the nearest whole number.)
Evaluate the definite integral.
64
dx

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