Explanation Given information: This problem shows how a surge can be modelled with a difference of exponential decay function. Formula used: The equation for the surge curve is y = a t e − b t , for positive constants a and b, increases rapidly and then decreases toward zero with a maximum at t = 1 b and the maximum is y = a b e . The function f ( t ) = e − t − e − 2 t is the vertical difference of the two. The graphs of e − t and e − 2 t : To determine (b) To find: The critical points and inflection points of f.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 4.8, Problem 9P

To determine

(a)

To explain:

Why the graph of f(t)=e−t−e−2t has the shape of a surge, using the graphs of e−t and e−2t.

To determine

(b)

To find:

The critical points and inflection points of f.

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Chapter 4.8, Problem 8P

Chapter 4.8, Problem 10P

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Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

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(a) To explain: Why the graph of f ( t ) = e − t − e − 2 t has the shape of a surge, using the graphs of e − t and e − 2 t .

Solution Summary: The author explains how the graph of f(t)=e-t-2t has the shape of a surge — it is the vertical difference of the two graphs.

Videos

(a)

To explain:

Why the graph of f(t)=e−t−e−2t has the shape of a surge, using the graphs of e−t and e−2t.

(b)

To find:

The critical points and inflection points of f.

Want to see the full answer?

Chapter 4 Solutions

(a) To explain: Why the graph of f ( t ) = e − t − e − 2 t has the shape of a surge, using the graphs of e − t and e − 2 t .

Solution Summary: The author explains how the graph of f(t)=e-t-2t has the shape of a surge — it is the vertical difference of the two graphs.

Videos

(a) To explain: Why the graph of f(t)=e−t−e−2t has the shape of a surge, using the graphs of e−t and e−2t.

(b) To find: The critical points and inflection points of f.

Want to see the full answer?

Chapter 4 Solutions

(a)

To explain:

Why the graph of f(t)=e−t−e−2t has the shape of a surge, using the graphs of e−t and e−2t.

(b)

To find:

The critical points and inflection points of f.