The concentration C(t) of a drug in the bloodstream t hoursafter it has been injected is

Chapter 4, Problem 52

(choose chapter or problem)

The concentration \(C(t)\) of a drug in the bloodstream \(t\) hours after it has been injected is commonly modeled by an equation of the form

                                         \(C(t)=\frac{K\left(e^{-b t}-e^{-a t}\right)}{a-b}\)

where \(K>0\) and \(a>b>0\)

(a) At what time does the maximum concentration occur?

(b) Let \(K=1\) for simplicity, and use a graphing utility to check your result in part (a) by graphing \(C(t)\) for various values of \(a\) and \(b\).

Equation Transcription:

Text Transcription:

C(t)

t

C(t)=K(e^-bt-e^-at/a-b

K>0

a>b>0

K=1

C(t)

a

b

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