   Chapter 12.3, Problem 44E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Concentration of a drug Suppose that the rate at which the concentration of a drug in the blood changes with respect to time t is given by C ' ( t ) = c b − a ( b e − b t − a e − a t ) , t ≥ 0 where a, b, and c are constants depending on the drug administered, with b > a. Assuming that C ( t ) =   0 when t = 0, find the formula for the concentration of the drug in the blood at any time t.

To determine

To calculate: The formula of concentration of the drug in the blood at any time t where the rate of concentration of a drug in the blood changes with respect to time t is given as:

C(t)=cba(bebtaeat),t0.

Where a,b&c are constant depending on the drug administered, with b>a.

Explanation

Given Information:

The rate of concentration of a drug in the blood changes with respect to time t is given as:

C(t)=cba(bebtaeat),t0; where a,b&c are constant depending on the drug administered, with b>a.

Assume that C(t)=0 when t=0.

Formula used:

If u is a function of x, then euudx=eudu=eu+C

Calculation:

Integrate the provided function as:

C(t)=cba(bebtaeat)dtC(t)=cba(ebt+<

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