EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
3rd Edition
ISBN: 9781285607160
Author: Larson
Publisher: CENGAGE CO
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Concept explainers

Limits
When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…
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Chapter 3, Problem 41CLT

a.

To determine

Draw a scatter plot for the given table using graphing utility.

a.

Expert Solution
Check Mark

Explanation of Solution

Given:

The given table is

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 1

  s represents the sales of lottery tickets (in billion dollar) and t represents the year.

Calculation:

By the use of graphing utility. The scatter plot for the given table is

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 2

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 3

b.

To determine

Find a cubic model for the given data using regression feature of graphing utility.

b.

Expert Solution
Check Mark

Answer to Problem 41CLT

The cubic model is s=−0.01715t3+0.119t2+2.215t+36.8 .

Explanation of Solution

Given:

The given table is

  s represents the sales of lottery tickets (in billion dollar) and t represents the year.

Calculation:

By the use of graphing utility. The scatter plot for the given table is

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 4

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 5

Using the graphing utility, the cubic model is

  y=ax3+bx2+cx+da=−0.01715b=0.119c=2.215d=36.8s=−0.01715t3+0.119t2+2.215t+36.8

Hence the cubic model is s=−0.01715t3+0.119t2+2.215t+36.8 .

c.

To determine

Find a cubic model for the given data using regression feature of graphing utility.

c.

Expert Solution
Check Mark

Explanation of Solution

Given:

The given table is

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 6

  s represents the sales of lottery tickets (in billion dollar) and t represents the year.

Calculation:

By the use of graphing utility. The scatter plot for the given table is

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 7

Using the graphing utility, the cubic model is

  y=ax3+bx2+cx+da=−0.01715b=0.119c=2.215d=36.8s=−0.01715t3+0.119t2+2.215t+36.8

The graph of cubic model with scatter plot is given below.

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 8

The model is fit for the given data.

d.

To determine

Find the sales of lottery tickets in the given year.

d.

Expert Solution
Check Mark

Answer to Problem 41CLT

The result is not reasonable

Explanation of Solution

Given:

The given table is

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 9

  s represents the sales of lottery tickets (in billion dollar) and t represents the year. The given year is 2018 .

Calculation:

By the use of graphing utility. The scatter plot for the given table is

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 41CLT , additional homework tip 10

Using the graphing utility, the cubic model is

  y=ax3+bx2+cx+da=−0.01715b=0.119c=2.215d=36.8s=−0.01715t3+0.119t2+2.215t+36.8

Substitute the value of t=18 in the model.

  s=−0.01715t3+0.119t2+2.215t+36.8=−0.01715(18)3+0.119(18)2+2.215(18)+36.8=−100.0188+38.556+39.87+36.8=15.2

The result is not reasonable because the trend of the model to increase, not decrease.

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Chapter 3, Problem 40CLT
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Chapter 3, Problem 42CLT

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

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