a. Answer Explanation Given information: The table shows the colonial population estimates of the American colonies. Y e a r P o p u l a t i o n 1700 250 , 900 1710 331 , 700 1720 466 , 200 1730 629 , 400 1740 905 , 600 1750 1 , 170 , 800 1760 1 , 593 , 600 1770 2 , 148 , 100 1780 2 , 780 , 400 Calculation: Using the regression feature of a graphing utility. b. To determine Find a quadratic model for the data. Answer P = 400.88 t 2 − 1464.6 t + 291782 Explanation Given information: The table shows the colonial population estimates of the American colonies. Y e a r P o p u l a t i o n 1700 250 , 900 1710 331 , 700 1720 466 , 200 1730 629 , 400 1740 905 , 600 1750 1 , 170 , 800 1760 1 , 593 , 600 1770 2 , 148 , 100 1780 2 , 780 , 400 Calculation: Calculate quadratic model, Now with the use of t a n d p from the table the graphing utility we get, ( a + b t + c t 2 , x , y , t ) 2.917824242424546 × 10 5 − 1464.63636363636284 + 400.878787878787762 2 P = 400.88 t 2 − 1464.6 t + 291782 Hence, the required quadratic model is P = 400.88 t 2 − 1464.6 t + 291782 c. To determine Plot the models from parts ( a ) and ( b ) in the same viewing window Answer Explanation Given information: The table shows the colonial population estimates of the American colonies. Y e a r P o p u l a t i o n 1700 250 , 900 1710 331 , 700 1720 466 , 200 1730 629 , 400 1740 905 , 600 1750 1 , 170 , 800 1760 1 , 593 , 600 1770 2 , 148 , 100 1780 2 , 780 , 400 Calculation: Use the graphing utility to plot the data and the models from parts ( a ) and ( b ) in the same viewing window. d. To determine Identify the model, better fit for the data. Answer Exponential model is well fitted for the data. Explanation Given information: The table shows the colonial population estimates of the American colonies. Y e a r P o p u l a t i o n 1700 250 , 900 1710 331 , 700 1720 466 , 200 1730 629 , 400 1740 905 , 600 1750 1 , 170 , 800 1760 1 , 593 , 600 1770 2 , 148 , 100 1780 2 , 780 , 400 Predict the population of the United States in 2020 . Calculation: From the graph we can say that exponential model is well fitted for the data, we can use this model to predict population of the United States in 2020 since it is increasing rapidly and approaching infinity. Hence, exponential model is well fitted for the data.

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3, Problem 15PS

To determine

Find an exponential model for the data using the regression feature of a graphing utility.

Expert Solution

Answer to Problem 15PS

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 15PS , additional homework tip 1

Explanation of Solution

Given information:

The table shows the colonial population estimates of the American colonies.

YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,10017802,780,400

Calculation:

Using the regression feature of a graphing utility.

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 15PS , additional homework tip 2

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 15PS , additional homework tip 3

To determine

Find a quadratic model for the data.

Expert Solution

Answer to Problem 15PS

P=400.88t2−1464.6t+291782

Explanation of Solution

Given information:

The table shows the colonial population estimates of the American colonies.

YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,10017802,780,400

Calculation:

Calculate quadratic model,

Now with the use of t and p from the table the graphing utility we get,

(a+bt+ct2,x,y,t)2.917824242424546×105−1464.63636363636284+400.8787878787877622P=400.88t2−1464.6t+291782

Hence, the required quadratic model is P=400.88t2−1464.6t+291782

To determine

Plot the models from parts (a) and (b) in the same viewing window

Expert Solution

Answer to Problem 15PS

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 15PS , additional homework tip 4

Explanation of Solution

Given information:

The table shows the colonial population estimates of the American colonies.

YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,10017802,780,400

Calculation:

Use the graphing utility to plot the data and the models from parts (a) and (b) in the same viewing window.

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 15PS , additional homework tip 5

To determine

Identify the model, better fit for the data.

Expert Solution

Answer to Problem 15PS

Exponential model is well fitted for the data.

Explanation of Solution

Given information:

The table shows the colonial population estimates of the American colonies.

YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,10017802,780,400

Predict the population of the United States in 2020 .

Calculation:

From the graph we can say that exponential model is well fitted for the data, we can use this model to predict population of the United States in 2020 since it is increasing rapidly and approaching infinity.

Hence, exponential model is well fitted for the data.

Chapter 3, Problem 14PS

Chapter 3, Problem 16PS

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

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