An individual is given a dose of Q units of a certain drug. the amount that remains in the bloodstream at the end of t minutes and Qe−ct, with c > 0. Suppose that the same dose is administered at successive intervals of T minutes. (a) Using series, express the amount A(k) of the drug in the bloodstream immediately after the K-th dose. (b) Find an upper bound for the amount of drug in the bloodstream after an arbitrary number of doses. (c) Find the shortest time between doses that ensures that A(k) does not exceed a certain level M, M > Q.

An individual is given a dose of Q units of a certain drug. the amount that remains in the bloodstream at the end of t minutes and Qe−ct, with c > 0. Suppose that the same dose is administered at successive intervals of T minutes. (a) Using series, express the amount A(k) of the drug in the bloodstream immediately after the K-th dose. (b) Find an upper bound for the amount of drug in the bloodstream after an arbitrary number of doses. (c) Find the shortest time between doses that ensures that A(k) does not exceed a certain level M, M > Q.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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Question

An individual is given a dose of Q units of a certain drug. the amount that remains in the bloodstream at the end of t minutes and Qe^−ct, with c > 0. Suppose that the same dose is administered at successive intervals of T minutes.

(a) Using series, express the amount A(k) of the drug in the bloodstream immediately after the K-th dose.
(b) Find an upper bound for the amount of drug in the bloodstream after an arbitrary number of doses.
(c) Find the shortest time between doses that ensures that A(k) does not exceed a certain level M, M > Q.

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