Explanation Given information: The rate of change of volume is given as, d V d t = k V 2 3 and initially the volume of the spherical cell is 0. Formula used: The logarithmic rule of integrals, ∫ 1 x d x = ln | x | + C where x ≠ 0 . The natural logarithm property, log a b = y ⇒ b = a y . Calculation: Consider the provided rate of change of the volume, d V d t = k V 2 3 . Rewrite the provided differential equation, V − 2 3 d V = k d t . Integrate both side of the equation as: ∫ V − 2 3 d V = ∫ k d t . Now, use the logarithmic rule of integrals to get, ∫ V − 2 3 d V = ∫ k d t V − 2 3 + 1 <

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 12.5, Problem 55E

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To calculate: The volume of the spherical cell as a function of time t, when the rate of change of volume is given as, dVdt=kV23

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Chapter 12.5, Problem 54E

Chapter 12.5, Problem 56E

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Chapter 12 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 12.1 - 1. True or false: (a) (b) Ch. 12.1 - Prob. 2CP Ch. 12.1 - 1. If what is Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...

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The volume of the spherical cell as a function of time t , when the rate of change of volume is given as, d V d t = k V 2 3

Solution Summary: The author calculates the volume of the spherical cell as a function of time t, using the logarithmic rule of integrals.

To calculate: The volume of the spherical cell as a function of time t, when the rate of change of volume is given as, dVdt=kV23

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Chapter 12 Solutions