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A mathematical model for the rate at which a drug disseminates into the bloodstream is given by dx =r - kx, dt where r and k are positive constants. The function x(t) describes the concentration of the drug in the bloodstream at time t. (a) Since the DE is autonomous, use the phase portrait concept of Section 2.1 to find the limiting value of x(t) as t → ∞. lim x(t) = t- 00 (b) Solve the DE subject to x(0) = 0. x(t) = Sketch the graph of x(t) and verify your prediction in part (a). k k At what time is the concentration one-half this limiting value?

A mathematical model for the rate at which a drug disseminates into the bloodstream is given by dx =r - kx, dt where r and k are positive constants. The function x(t) describes the concentration of the drug in the bloodstream at time t. (a) Since the DE is autonomous, use the phase portrait concept of Section 2.1 to find the limiting value of x(t) as t → ∞. lim x(t) = t- 00 (b) Solve the DE subject to x(0) = 0. x(t) = Sketch the graph of x(t) and verify your prediction in part (a). k k At what time is the concentration one-half this limiting value?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...
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A mathematical model for the rate at which a drug disseminates into the bloodstream is given by dx =r - kx, dt where r and k are positive constants. The function x(t) describes the concentration of the drug in the bloodstream at time t. (a) Since the DE is autonomous, use the phase portrait concept of Section 2.1 to find the limiting value of x(t) as t → ∞. lim x(t) = (b) Solve the DE subject to x(0) = 0. x(t) = Sketch the graph of x(t) and verify your prediction in part (a). r k r k X X t At what time is the concentration one-half this limiting value?
Transcribed Image Text:A mathematical model for the rate at which a drug disseminates into the bloodstream is given by dx =r - kx, dt where r and k are positive constants. The function x(t) describes the concentration of the drug in the bloodstream at time t. (a) Since the DE is autonomous, use the phase portrait concept of Section 2.1 to find the limiting value of x(t) as t → ∞. lim x(t) = (b) Solve the DE subject to x(0) = 0. x(t) = Sketch the graph of x(t) and verify your prediction in part (a). r k r k X X t At what time is the concentration one-half this limiting value?
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