Explanation Given Information: A liquid carries a drug into a 160 -cc organ at a rate of 4 cc/s and leaves the organ at same rate and the concentration of drug in liquid is 0.1 g/cc. Formula used: The separable equation is: g ( y ) d y = f ( x ) d x Integration both side yield the solution is, According to the logarithmic rule of integrals, ∫ 1 x d x = ln | x | + C Calculation: As it is provided that a liquid carries a drug into a 160 -cc organ at a rate of 4 cc/s and leaves the organ at same rate and the concentration of drug in liquid is 0.1 g/cc. Now, let x represent the amount of drug in the organ, then according to the provided information, the differential equation that represents the situation will be, the difference of rate of drug injection and the rate of drug ejection, that is, Now, the injection rate will be the amount of liquid multiplied by the concentration of drug in that liquid, that is, R i n = 4 ( 0.1 ) cc/s And, the rate of ejection if x g of drug is present in the organ will be, R o u t = x 120 ⋅ 4 cc/s Thus, the expression for rate will be, d x d t = R i n − R o u t = 4 ⋅ 0.1 − 4 ⋅ x 160 = 0.4 − x 40 = 16 − x 40 Thus, the differential equation will be, d x d t = 16 − x 40 The equation is in separable form

11th Edition

ISBN: 9781305713864

Author: HARSHBARGER

Publisher: CENGAGE L

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Chapter 12, Problem 22T

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To calculate: The amount of drug in the organ as a function of time if a liquid carries a drug into a 160-cc organ at a rate of 4 cc/s and leaves the organ at same rate and the concentration of drug in liquid is 0.1 g/cc.

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Chapter 12, Problem 21T

Chapter 13.1, Problem 1CP

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The amount of drug in the organ as a function of time if a liquid carries a drug into a 160 -cc organ at a rate of 4 cc/s and leaves the organ at same rate and the concentration of drug in liquid is 0.1 g/cc.

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

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To calculate: The amount of drug in the organ as a function of time if a liquid carries a drug into a 160-cc organ at a rate of 4 cc/s and leaves the organ at same rate and the concentration of drug in liquid is 0.1 g/cc.

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Chapter 12 Solutions