   Chapter 12, Problem 22T ### 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

# Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 160-cc organ at the rate of 4 cc/sec and leaves at the same rate. 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 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.

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)dy=f(x)dx

Integration both side yield the solution is,

According to the logarithmic rule of integrals,

1xdx=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,

Rin=4(0.1)cc/s

And, the rate of ejection if x g of drug is present in the organ will be,

Rout=x1204cc/s

Thus, the expression for rate will be,

dxdt=RinRout=40.14x160=0.4x40=16x40

Thus, the differential equation will be,

dxdt=16x40

The equation is in separable form

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 5-8, find the limit. limx02xx+(x)2x

Calculus: An Applied Approach (MindTap Course List)

#### In Exercises 1124, find the indicated limits, if they exist. 20. limx1x1x1

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### True or False: is a geometric series.

Study Guide for Stewart's Multivariable Calculus, 8th

#### The appropriate option for the value of (123).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 