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

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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.

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Chapter 9.5, Problem 35E

Chapter 9.5, Problem 37E

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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...

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

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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.

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