Explanation Given Information: The rate of liquid into a 120-cc organ by a drug is 4 cc / s and the concentration of drug in liquid in 4 g / s . 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 a drug carries liquid at a rate of 4 cc / s . Now, let x represent the amount of drug in the organ, then according to the provided information, the differential equation that represents the situation is, d x d t = 4 ⋅ 3 − 4 ⋅ x 120 = 360 − x 30 Rewrite the above differential equation, d x 360 − x = d t 30 Integrate both sides to get, ∫ d x 360 − x = ∫ d t 30 Now, use the logarithmic rule of integrals to get, ∫ d x 360 − x =

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, Problem 48RE

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To calculate: The amount of drug in the organ as a function of time when the rate of liquid into a 120-cc organ by a drug is 4 cc/s and the concentration of drug in liquid in 4 g/s.

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Chapter 12, Problem 47RE

Chapter 12, Problem 49RE

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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 amount of drug in the organ as a function of time when the rate of liquid into a 120-cc organ by a drug is 4 cc / s and the concentration of drug in liquid in 4 g / s .

Solution Summary: The author calculates the amount of drug in the organ as a function of time, using the logarithmic rule of integrals.

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To calculate: The amount of drug in the organ as a function of time when the rate of liquid into a 120-cc organ by a drug is 4 cc/s and the concentration of drug in liquid in 4 g/s.

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Chapter 12 Solutions