a . Answer Year Population 1980 104,752 1990 143,251 2000 195,899 2010 267,896 Explanation Given: The population P (in thousands) is given by the model: P = 76.6 e 0.0313 t Where t represents the year, with t = 1 corresponding to 1971. Calculation: Consider the given population model: P = 76.6 e 0.0313 t ….. (1) Now, as t = 1 corresponding to 1971, so t = 10 corresponds to 1980, t = 20 corresponding to 1990, so t = 30 corresponds to 2000, t = 40 corresponds to 2010. The population in year 1980: Substitute t = 10 in equation (1), P = 76.6 e 0.0313 × 10 ≈ 104.752 The population in year 1990: Substitute t = 20 in equation (1), P = 76.6 e 0.0313 × 20 ≈ 143.251 The population in year 2000: Substitute t = 30 in equation (1), P = 76.6 e 0.0313 × 30 ≈ 195.899 The population in year 2010: Substitute t = 40 in equation (1), P = 76.6 e 0.0313 × 20 ≈ 267.896 Since, the given population model gives the population in thousands, so the actual population is obtained by multiplying the value obtained for that year by 1000. Thus, the complete table is: Year Population 1980 104,752 1990 143,251 2000 195,899 2010 267,896 b. To determine To find: the year when the population will reach 360,000 Answer 2019 Explanation Given: The population P (in thousands) is given by the model: P = 76.6 e 0.0313 t ….. (1) Where t represents the year, with t = 1 corresponding to 1971. Formula used: ln e x = x Calculation: The given population model gives the population in thousands Substitute P = 360 in equation (1), 360 = 76.6 e 0.0313 t e 0.0313 t = 360 76.6 Take natural logarithm on both sides, ln e 0.0313 t = ln ( 360 76.6 ) 0.0313 t = ln ( 360 76.6 ) t = 1 0.0313 ln ( 360 76.6 ) t ≈ 49.44 Now, t = 1 corresponding to 1971, so it can be said that during 49 t h year population will be 360,000. That is, in the year 2019 population will be 360,000. c. To determine To explain: is the model valid for long-term predictions of the population Answer No Explanation Observe the table obtained in part (a), Year Population 1980 104,752 1990 143,251 2000 195,899 2010 267,896 It can be said that according to this population model, as the time t increases, the population is increasing very rapidy without any bound.

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3.5, Problem 29E

a .

To determine

To complete: the table given below:

Year Population
1980
1990
2000
2010

a .

Expert Solution

Answer to Problem 29E

Year	Population
1980	104,752
1990	143,251
2000	195,899
2010	267,896

Explanation of Solution

Given:

The population P (in thousands) is given by the model:

P=76.6e0.0313t

Where t represents the year, with t=1 corresponding to 1971.

Calculation:

Consider the given population model:

P=76.6e0.0313t ….. (1)

Now, as t=1 corresponding to 1971, so t=10 corresponds to 1980, t=20 corresponding to 1990, so t=30 corresponds to 2000, t=40 corresponds to 2010.

The population in year 1980:

Substitute t=10 in equation (1),

P=76.6e0.0313×10≈104.752

The population in year 1990:

Substitute t=20 in equation (1),

P=76.6e0.0313×20≈143.251

The population in year 2000:

Substitute t=30 in equation (1),

P=76.6e0.0313×30≈195.899

The population in year 2010:

Substitute t=40 in equation (1),

P=76.6e0.0313×20≈267.896

Since, the given population model gives the population in thousands, so the actual population is obtained by multiplying the value obtained for that year by 1000. Thus, the complete table is:

Year	Population
1980	104,752
1990	143,251
2000	195,899
2010	267,896

To determine

To find: the year when the population will reach 360,000

Expert Solution

Answer to Problem 29E

2019

Explanation of Solution

Given:

The population P (in thousands) is given by the model:

P=76.6e0.0313t ….. (1)

Where t represents the year, with t=1 corresponding to 1971.

Formula used:

lnex=x

Calculation:

The given population model gives the population in thousands Substitute P=360 in equation (1),

360=76.6e0.0313te0.0313t=36076.6

Take natural logarithm on both sides,

lne0.0313t=ln(36076.6)0.0313t=ln(36076.6)t=10.0313ln(36076.6)t≈49.44

Now, t=1 corresponding to 1971, so it can be said that during 49^t^h year population will be 360,000.

That is, in the year 2019 population will be 360,000.

To determine

To explain: is the model valid for long-term predictions of the population

Expert Solution

Answer to Problem 29E

Explanation of Solution

Observe the table obtained in part (a),

Year	Population
1980	104,752
1990	143,251
2000	195,899
2010	267,896

It can be said that according to this population model, as the time t increases, the population is increasing very rapidy without any bound.

Chapter 3.5, Problem 28E

Chapter 3.5, Problem 30E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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the table given below: Year Population 1980 1990 2000 2010

Concept explainers

Videos

To complete: the table given below: Year Population 1980 1990 2000 2010

Answer to Problem 29E

Explanation of Solution

To find: the year when the population will reach 360,000

Answer to Problem 29E

Explanation of Solution

To explain: is the model valid for long-term predictions of the population

Answer to Problem 29E

Explanation of Solution

Chapter 3 Solutions

To complete: the table given below:

Year Population
1980
1990
2000
2010