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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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Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 6

Graphing with Calculus and Calculators

Derivatives

Differentiation

Volume

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

01:12

The family of functions $f…

02:24

02:13

The "family of functi…

06:43

Graph the following single…

02:05

Investigate the family of …

03:27

02:26

02:37

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