a. Explanation Given: The volume of the blood is four liter which initial concentration is zero. This implies V = 4 L . The blood contains the concentration 500 m g / L with drug solution and the inflow rate of the blood is 0.06 L . That is, C i = 500 m g / L and R = 0.06 L . Calculation: The stirred tank reaction is computed as follows, m ′ ( t ) = − 0.06 4 m ( t ) + ( 500 ) ( 0.06 ) m ′ ( t ) = − 0.015 m ( t ) + 30 Rewrite the above differential equation as follows, m ′ ( t ) − 0.015 m ( t ) + 30 = 1 Integrate on both sides of the above expression with respect to t . That is, ∫ m ′ ( t ) − 0.015 m ( t ) + 30 d t = ∫ 1 d t − 1 0.015 ∫ 0.015 m ′ ( t ) d t 0 b. To determine To find: The initial value problem of the given function and graph the solution for both the mass of the drug and the concentration of the drug. c. To determine To find: The steady state mass of the drug in the blood. d. To determine The time in which the drug mass reach 90 % of steady state level.

Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package

3rd Edition

ISBN: 9780136207764

Author: Briggs, William, Cochran, Lyle, Gillett, Bernard, SCHULZ, Eric

Publisher: PEARSON

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 9.5, Problem 36E

To determine

To find: The initial value problem of the given problem which indicate the mass of the drug in blood, t≥0 .

To determine

To find: The initial value problem of the given function and graph the solution for both the mass of the drug and the concentration of the drug.

To determine

To find: The steady state mass of the drug in the blood.

To determine

The time in which the drug mass reach 90% of steady state level.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.5, Problem 35E

Chapter 9.5, Problem 37E

Students have asked these similar questions

Solve this question and show steps.

u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 9 Solutions

Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package

Ch. 9.1 - What are the orders of the equations in Example 2?...Ch. 9.1 - What is the solution of the initial value problem...Ch. 9.1 - Solve the initial value problem in Example 4a with...Ch. 9.1 - Suppose the initial conditions in Example 5a are...Ch. 9.1 - In Example 7, if the height function were given by...Ch. 9.1 - Consider the differential equation y(t) + 9y(t) =...Ch. 9.1 - If the general solution of a differential equation...Ch. 9.1 - Does the function y(t) = 2t satisfy the...Ch. 9.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. 9.1 - The solution to the initial value problem y(t) = 2...

Additional Math Textbook Solutions

Find more solutions based on key concepts

Find how many SDs above the mean price would be predicted to cost.

Intro Stats, Books a la Carte Edition (5th Edition)

Answer each of the following and explain your answer. a. How many lines can contain a particular segment? b. Ho...

A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

CHECK POINT 1 Find a counterexample to show that the statement The product of two two-digit numbers is a three-...

Thinking Mathematically (6th Edition)

In Exercises 25–28, use the confidence interval to find the margin of error and the sample mean. 25. (12.0, 14....

Elementary Statistics: Picturing the World (7th Edition)

17. Redesign of Ejection Seats When women were finally allowed to become pilots of fighter jets, engineers need...

Elementary Statistics (13th Edition)

If n is a counting number, bn, read______, indicates that there are n factors of b. The number b is called the_...

Algebra and Trigonometry (6th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The initial value problem of the given problem which indicate the mass of the drug in blood, t ≥ 0 .

Solution Summary: The author explains the initial value problem of the given problem which indicate the mass of drug in blood, tge 0.

Concept explainers

Videos

To find: The initial value problem of the given problem which indicate the mass of the drug in blood, t≥0 .

To find: The initial value problem of the given function and graph the solution for both the mass of the drug and the concentration of the drug.

To find: The steady state mass of the drug in the blood.

The time in which the drug mass reach 90% of steady state level.

Want to see the full answer?

Chapter 9 Solutions

Additional Math Textbook Solutions