Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Question
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Chapter 3, Problem 79RE

a.

To determine

Determine the domain of the function in the context of the problem.

a.

Expert Solution
Check Mark

Answer to Problem 79RE

  (0,18000)

Explanation of Solution

Given information:

The time t (in minutes) for a small plane to climb to an altitude of h feet is modelled by t=50log[18,000/(18,000−h)] where 18,000 feet is the plane’s absolute ceiling.

Determine the domain of the function in the context of the problem.

Calculation:

The logarithm is defined only for positive real number so that,

  18,000(18,000−h)≥0

This is possible only when h is in the range of (0−18000)

Hence the domain of the function is, (0,18000)

b.

To determine

Use a graphing utility to graph the function and identify any asymptotes.

b.

Expert Solution
Check Mark

Answer to Problem 79RE

  h=18000

Explanation of Solution

Given information:

The time t (in minutes) for a small plane to climb to an altitude of h feet is modelled by t=50log[18,000/(18,000−h)] where 18,000 feet is the plane’s absolute ceiling.

Use a graphing utility to graph the function and identify any asymptotes.

Calculation:

The graph the function is,

  Precalculus with Limits, Chapter 3, Problem 79RE

Hence, from the graph vertical asymptotes is, h=18000

c.

To determine

What can be said about the time required to increase its altitude?

c.

Expert Solution
Check Mark

Answer to Problem 79RE

  increased

Explanation of Solution

Given information:

The time t (in minutes) for a small plane to climb to an altitude of h feet is modelled by t=50log[18,000/(18,000−h)] where 18,000 feet is the plane’s absolute ceiling.

As the plane approaches its absolute ceiling, what can be said about the time required to increase its altitude?

Calculation:

As the plane is at a slower rate so that required time is increased.

Hence, the time is increased .

d.

To determine

Find the time it takes for the plane to climb to an altitude of 4000ft .

d.

Expert Solution
Check Mark

Answer to Problem 79RE

  5.46minutes

Explanation of Solution

Given information:

The time t (in minutes) for a small plane to climb to an altitude of h feet is modelled by t=50log[18,000/(18,000−h)] where 18,000 feet is the plane’s absolute ceiling.

Find the time it takes for the plane to climb to an altitude of 4000ft .

Calculation:

Put h=4000 in the given model,

  t=50log[18,000/(18,000−h)]

  t=50log[18,000/(18,000−4000)]t=5.46minutes

Hence, the time required is 5.46minutes .

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Chapter 3, Problem 78RE
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Chapter 3, Problem 80RE

Chapter 3 Solutions

Precalculus with Limits

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