   Chapter 12.5, Problem 51E ### 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 with concentration 0.1 g/cc into a 200-cc organ at a rate of 5cc/s and leaves the organ at the same rate. If initially there is 10 g of the drug in the organ, find the amount of drug in the organ as a function of time t.

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 200-cc organ by drugs is cc/s and the initial rate of concentration of the drug in the organ is 0.1 g/cc.

Explanation

Given information:

The rate of liquid to enter and leave the 200-cc organ by drugs is cc/s and the initial rate of concentration of the drug in the organ is 0.1 g/cc and the initially there is 10 g drug in the organ.

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 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=5(0.1)5(x200)dxdt=20x40

Rewrite the above differential equation,

dx20x=dt40

Integrate both side of the equation as:

dx20x=dt40

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