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# The family of functions $f(t) = C(e^{-at} - e^{-bt})$, where $a$, $b$, and $C$ are positive numbers and $b > a$, has been used to model the concentration of a drug injected into the bloodstream at time $t = 0$. Graph several members of this family. What do they have in common? For fixed values of $C$ and $a$, discover graphically what happens as $b$ decreases. Then use calculus to prove what you have discovered.

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Arizona State University

Derivatives

Differentiation

Volume

Lectures

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