   Chapter 12, Problem 48RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Drug in an organ Suppose that a liquid carries a drug into a 120-cc organ at a rate of 4 cc/s and leaves the organ at the same rate. If initially there is no drug in the organ and if the concentration of drug in the liquid is 3 g/cc, find the amount of drug in the organ as a function of time.

To determine

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.

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, 1xdx=ln|x|+C where x0.

The natural logarithm property,

logab=yb=ay.

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,

dxdt=434x120=360x30

Rewrite the above differential equation,

dx360x=dt30

Integrate both sides to get,

dx360x=dt30

Now, use the logarithmic rule of integrals to get,

dx360x=

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