PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Chapter 3.4, Problem 134E

a.

To determine

To find: the graph of the function V=6.7e−48.1/t .

a.

Expert Solution
Check Mark

Explanation of Solution

Given information :

Given function V=6.7e−48.1/t .

Graph:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.4, Problem 134E

b.

To determine

the horizontal asymptote of the function V=6.7e−48.1/t . And its meaning in the context of the problem.

b.

Expert Solution
Check Mark

Answer to Problem 134E

Horizontal asymptote is at x=6.7 . Which is the upper bound of the function V(t) .

Explanation of Solution

Given information :

Given function V=6.7e−48.1/t .

The horizontal asymptote is the of V(t) for large t . That is,

  limt→∞V(t)=limt→∞6.7e−48.1/t=6.7limt→∞1e48.1/t=6.7×1e48.1∞=6.7×1e0=6.7×11=6.7

Hence the horizontal asymptote is at x=6.7 . Which means the upper bound of V(t) is x=6.7 . The function will not reach the line x=6.7 .

c.

To determine

To find: the time necessary to obtain a yield of 1.3 million cubic feet.

c.

Expert Solution
Check Mark

Answer to Problem 134E

The time required 29.33 years.

Explanation of Solution

Given information :

Given function V=6.7e−48.1/t .

When V(t)=1.3 we get,

  V(t)=1.3⇒6.7e−48.1/t=1.3⇒e−48.1/t=1.36.7  (Taking log on both side)⇒log(e−48.1/t)=log(1.36.7)⇒−48.1tlog(e)=log(1367)⇒t=−48.1×log(e)log(1367)⇒t≈29.33 (Rund up to two decimal places)

So the time required 29.33 years.

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Chapter 3.4, Problem 133E
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Chapter 3.4, Problem 135E

Chapter 3 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
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Prob. 27CTCh. 3 - Prob. 28CTCh. 3 - Prob. 29CTCh. 3 - Prob. 30CTCh. 3 - Prob. 1STPCh. 3 - Prob. 2STPCh. 3 - Prob. 3STPCh. 3 - Prob. 4STPCh. 3 - Prob. 5STPCh. 3 - Prob. 6STPCh. 3 - Prob. 7STPCh. 3 - Prob. 8STPCh. 3 - Prob. 9STPCh. 3 - Prob. 10STPCh. 3 - Prob. 11STPCh. 3 - Prob. 12STPCh. 3 - Prob. 13STPCh. 3 - Prob. 14STPCh. 3 - Prob. 15STPCh. 3 - Prob. 16STPCh. 3 - Prob. 17STPCh. 3 - Prob. 18STPCh. 3 - Prob. 19STPCh. 3 - Prob. 20STPCh. 3 - Prob. 21STPCh. 3 - Prob. 22STPCh. 3 - Prob. 23STPCh. 3 - Prob. 24STPCh. 3 - Prob. 25STPCh. 3 - Prob. 26STP
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