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– 2 years ago **files (1)** – ## Week3EndofWeekAssignment-GrowthModels.docx **## Week3EndofWeekAssignment-GrowthModels.docx** **Exponential Growth—U.S. Population and World Population** ### Mathematical Modeling Exercise 1 Callie and Joe are examining the population data in the graphs below for a hi…
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– 2 years ago
**files (1)**
– ## Week3EndofWeekAssignment-GrowthModels.docx
**## Week3EndofWeekAssignment-GrowthModels.docx**
**Exponential Growth—U.S. Population and World Population**
### Mathematical Modeling Exercise 1
Callie and Joe are examining the population data in the graphs below for a history report. Their comments are as follows:
Callie: It looks like the U.S. population grew the same amount as the world population, but that can’t be right, can it? Joe: Well, I don’t think they grew by the same
_amount_, but they sure grew at about the same rate. Look at the slopes.
**Population (in millions)**
**Population (in millions)**
**U.S. Population**
300
250
200
150
100
50
0
1950 1960 1970 1980 1990 2000
**Year**
**World Population**
7000
6000
5000
4000
3000
2000
1000
0
1950 1960 1970 1980 1990 2000
**Year**
1a. Is Callie’s observation correct? Why or why not?
1b. Is Joe’s observation correct? Why or why not?
2a. Show your work.
Use the World Population graph to estimate the percent increase in world population from 1950 to 2000.
Now, use the U.S. Population graph to estimate the percent increase in the U.S. population for the same time period.
3a. How does the percent increase for the world population compare to that for the U.S. population over the same time period, 1950 to 2000?
3b. Do the graphs above seem to indicate linear or exponential population growth? Explain your response.
4. Write an explicit formula for the function that models the world population growth from 1950
to 2000 based on the information in the graph. Assume that the population (in millions) in 1950
was 2,500 and in 2000 was 6,000. Use 𝑡 to represent the number of years after 1950.
### Mathematical Modeling Exercise 2 **World Population** 7000 6000 5000 4000 3000 2000 1000 0 1700 1750 1800 1850 **Year** 1900 1950 2000 **Population (in millions)**
5. How is this graph similar to the World Population graph in Mathematical Modeling Exercise 1? How is it different?
6a. Does the behavior of the graph from 1950 to 2000 match that shown on the graph in Mathematical Modeling Exercise 1? Explain your answer.
6b. Why is the graph from Mathematical Modeling Exercise 1 somewhat misleading?
**## Week3EndofWeekAssignment-GrowthModels.docx**
**Exponential Growth—U.S. Population and World Population**
### Mathematical Modeling Exercise 1
Callie and Joe are examining the population data in the graphs below for a history report. Their comments are as follows:
Callie: It looks like the U.S. population grew the same amount as the world population, but that can’t be right, can it? Joe: Well, I don’t think they grew by the same
_amount_, but they sure grew at about the same rate. Look at the slopes.
**Population (in millions)**
**Population (in millions)**
**U.S. Population**
300
250
200
150
100
50
0
1950 1960 1970 1980 1990 2000
**Year**
**World Population**
7000
6000
5000
4000
3000
2000
1000
0
1950 1960 1970 1980 1990 2000
**Year**
1a. Is Callie’s observation correct? Why or why not?
1b. Is Joe’s observation correct? Why or why not?
2a. Show your work.
Use the World Population graph to estimate the percent increase in world population from 1950 to 2000.
Now, use the U.S. Population graph to estimate the percent increase in the U.S. population for the same time period.
3a. How does the percent increase for the world population compare to that for the U.S. population over the same time period, 1950 to 2000?
3b. Do the graphs above seem to indicate linear or exponential population growth? Explain your response.
4. Write an explicit formula for the function that models the world population growth from 1950
to 2000 based on the information in the graph. Assume that the population (in millions) in 1950
was 2,500 and in 2000 was 6,000. Use 𝑡 to represent the number of years after 1950.
### Mathematical Modeling Exercise 2 **World Population** 7000 6000 5000 4000 3000 2000 1000 0 1700 1750 1800 1850 **Year** 1900 1950 2000 **Population (in millions)**
5. How is this graph similar to the World Population graph in Mathematical Modeling Exercise 1? How is it different?
6a. Does the behavior of the graph from 1950 to 2000 match that shown on the graph in Mathematical Modeling Exercise 1? Explain your answer.
6b. Why is the graph from Mathematical Modeling Exercise 1 somewhat misleading?
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