Program Explanation Given information: The differential equation for the sugar is d A d t = − k A . After 1 minute 25 % of the sugar is dissolved. Calculation: The given differential equation is as follows, d A d t = − k A Here, A is the amount that remains undissolved after t minutes. Now use the method of separation of the variable to solve the above differential equation. d A d t = k A d T k A = d t Now integrate both sides. d A k A = d t ∫ d A A = ∫ − k d t ln A = − k t + c 1 A = A 0 e − k t Therefore, the amount of the undissolved sugar function is as follows, A ( t ) = A 0 e − k t ........ (1) It is given that after 1 minute 25 % of the sugar is dissolved. Therefore, the amount of undissolved sugar can be evaluated as, A 1 = A 0 − 25 % A 0 A 1 = A 0 − 1 4 A 0 A 1 = 3 4 A 0 Therefore, the condition is A ( 1 ) = 3 4 A 0

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

Author: Edwards, C., Penney, David, Calvis

Publisher: PEARSON

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 1.4, Problem 44P

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Program Description: Purpose of the problem is to find the time at which half of the sugar dissolve.

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Chapter 1.4, Problem 43P

Chapter 1.4, Problem 45P

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Chapter 1 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

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Program Description: Purpose of the problem is to find the time at which half of the sugar dissolve.

Solution Summary: The author explains that the problem is to find the time at which half of the sugar dissolves.

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Program Description: Purpose of the problem is to find the time at which half of the sugar dissolve.

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Chapter 1 Solutions