   Chapter 12.5, Problem 50E ### 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 250-cc organ at a rate of 10cc/s and leaves the organ at the same rate. Suppose that the concentration of the drug entering is 0.15g/cc. Find the amount of drug in the organ as a function of time t if initially there is none in the organ.

To determine

To calculate: The amount of drugs in the organ as a function of time t when the rate of liquid to enter and leave the 250-cc organ by drugs is 10 cc/s and the initial rate of concentration of the drug in the organ is 0.15 g/cc.

Explanation

Given information:

The rate of liquid to enter and leave the 250-cc organ by drugs is 10 cc/s and the initial rate of concentration of the drug in the organ is 0.15 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 10 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=10(0.15)10(x250)=1.5x25=37.5x25

Rewrite the above differential equation,

dx37.5x=dt25

Integrate both side of the equation as:

dx37.5x=dt25

Now, use the logarithmic rule of integrals to get,

dx37

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