a. Explanation Given: The differential equation is y ′ ( t ) = − 0.02 y + 3 with its initial condition y ( 0 ) = 0 . Calculation: The differential equation is y ′ ( t ) = − 0.02 y + 3 . Solve the above the differential equation as follows, d y d t = − 0.02 y + 3 d y − 0.02 y + 3 = d t Integrate on both sides of the above expression as follows, ∫ d y − 0.02 y + 3 = ∫ d t − 1 0.02 ln ( − 0.02 y + 3 ) = t + c ln ( − 0.02 y + 3 ) = − 0.02 t + c Take exponential on both sides as follows, e ln ( − 0.02 y + 3 ) = e − 0.02 t + c − 0.02 y + 3 = c e − 0.02 t − 0.02 y = − 3 + c e − 0.02 t y ( t ) = − 3 − 0 b. To determine To find: The steady state-level of the drug. c. To determine To find: The steady state value of the drug such that the drug reaches 90 % .

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

3rd Edition

ISBN: 9780134996103

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 9.4, Problem 31E

To determine

To find: The initial value of the differential equation y′(t)=−0.02y+3 with its initial condition y(0)=0 and sketch the graph of its general solution.

To determine

To find: The steady state-level of the drug.

To determine

To find: The steady state value of the drug such that the drug reaches 90% .

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Chapter 9.4, Problem 30E

Chapter 9.4, Problem 33E

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Chapter 9 Solutions

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

Ch. 9.1 - What are the orders of the equations in Example 2?...Ch. 9.1 - Prob. 2QC Ch. 9.1 - Prob. 3QC Ch. 9.1 - Prob. 4QC Ch. 9.1 - In Example 7, if the height function were given by...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - The solution to the initial value problem y(t) = 2...

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The initial value of the differential equation y ′ ( t ) = − 0.02 y + 3 with its initial condition y ( 0 ) = 0 and sketch the graph of its general solution.

Solution Summary: The author explains the initial value of the differential equation yprime(t)=-0.02y+3 and sketch the graph of its general solution.

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To find: The initial value of the differential equation y′(t)=−0.02y+3 with its initial condition y(0)=0 and sketch the graph of its general solution.

To find: The steady state-level of the drug.

To find: The steady state value of the drug such that the drug reaches 90% .

Want to see the full answer?

Chapter 9 Solutions