Explanation Given: The differential equation is: d y d x = − 0.09 y and the conditions are: y = 100 at x = 0 Formula used: The formula for the integral of an inverse function is: ∫ 1 y d y = ln | y | + C Here, C is the integral constant. Also, the formula for an integral of a constant is, ∫ a d y = a y + C Here, a is a constant and C is an integration constant. If more than one integral is there in an expression then the constant of the integrals is replaced by a single constant. Property of logarithm: If, ln | y | = x + c Then, y = ± e x + c Calculation: Explanation: Consider the differential equation: d y d x = − 0.09 y General equation of the above expressions is: ∫ 1 y d y = − ∫ 0.09 d x Use the formulas of integral of an inverse function and a constant and solve

MyLab Math with Pearson eText -- Standalone Access Card -- for Mathematics with Applications in the Management, Natural, and Social Sciences (12th Edition)

12th Edition

ISBN: 9780134856551

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 13.7, Problem 26E

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Chapter 13.7, Problem 25E

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Chapter 13 Solutions

MyLab Math with Pearson eText -- Standalone Access Card -- for Mathematics with Applications in the Management, Natural, and Social Sciences (12th Edition)

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

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The general solution for the differential equation d y d x = − 0.09 y .

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