Explanation Given: Demand (in pounds) of coffee per week, whose price is p dollars per pound is given by, D ( p ) = 4374 p 2 Also, the price of coffee t weeks from now is: p ( t ) = 0.02 t 2 + 0.01 t + 6 Formula used: d d x ( x n ) = n x n − 1 By chain rule: d d t f [ u ( x ) ] = d d u f ( u ) d u d x Calculations: Now, Demand (in pounds) of coffee per week is given by, D ( p ) = 4374 p 2 And the price of coffee t weeks from now is: p ( t ) = 0.02 t 2 + 0.01 t + 6 , Then, by chain rule, the rate of change of weekly demand with respect to time is, d D d t = d D d p ⋅ d p d t = d d p ( 4374 p 2 ) d d t ( 0.02 t 2 + 0.01 t + 6 ) = [ 4374 d d p ( p − 2 ) ] [ 0.02 d d t ( t 2 ) + 0

Student's Solution Manual and Survival Manual for Calculus

6th Edition

ISBN: 9781465241658

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Differential Equations

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Chapter 3.5, Problem 47PS

To determine

To find:the rate of change of weekly demand of coffee with respect to time 10 weeks from now. Also find if the demand is increasing or decreasing

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Chapter 3 Solutions

Student's Solution Manual and Survival Manual for Calculus

Ch. 3.1 - Prob. 1PS Ch. 3.1 - Prob. 2PS Ch. 3.1 - Prob. 3PS Ch. 3.1 - Prob. 4PS Ch. 3.1 - Prob. 5PS Ch. 3.1 - Prob. 6PS Ch. 3.1 - Prob. 7PS Ch. 3.1 - Prob. 8PS Ch. 3.1 - Prob. 9PS Ch. 3.1 - Prob. 10PS

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the rate of change of weekly demand of coffee with respect to time 10 weeks from now. Also find if the demand is increasing or decreasing

Solution Summary: The author calculates the rate of change of weekly demand of coffee with respect to time 10 weeks from now.

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To find:the rate of change of weekly demand of coffee with respect to time 10 weeks from now. Also find if the demand is increasing or decreasing

Chapter 3 Solutions