Population (in millions) 500- 400- € 300- 200- 100- 0 (1.260) (3,300) (1,100) (2,200) Time (in years) A B (4,400) (3,150) Note: Graph not drawn to scale. Q Q The average growth rate of population A is (Simplify your answer.) The average growth rate of population B is (Simplify your answer.) b) If the calculation in part (a) were the only one made, would we detect the fact populations were growing differently? million people per year. O A. No, the unequal rates suggest similar growth patterns. O B. Yes, the unequal rates suggest different growth patterns. O C. No, the equal rates suggest similar growth patterns. O D. Yes, the equal rates suggest different growth patterns. million people per year. c) Find the average rates of change of each population as t changes from 0 to 1; from 2 to 3; from 3 to 4. Population 0 to 1 1 to 2 2 to 3 3 to 4 Complete the table with the average rates of change (in millions). A B I || d) For which population does the statement "the population grew consistently at million per year" convey accurate information? Why? O A. Population B, because it initially grew slower than population A. O B. Population A, because the average rate of change each year was 100. O C. Population A, because the average growth rate for the four years was 10 OD. Population B, because the average rate of change each year was 100.
Population (in millions) 500- 400- € 300- 200- 100- 0 (1.260) (3,300) (1,100) (2,200) Time (in years) A B (4,400) (3,150) Note: Graph not drawn to scale. Q Q The average growth rate of population A is (Simplify your answer.) The average growth rate of population B is (Simplify your answer.) b) If the calculation in part (a) were the only one made, would we detect the fact populations were growing differently? million people per year. O A. No, the unequal rates suggest similar growth patterns. O B. Yes, the unequal rates suggest different growth patterns. O C. No, the equal rates suggest similar growth patterns. O D. Yes, the equal rates suggest different growth patterns. million people per year. c) Find the average rates of change of each population as t changes from 0 to 1; from 2 to 3; from 3 to 4. Population 0 to 1 1 to 2 2 to 3 3 to 4 Complete the table with the average rates of change (in millions). A B I || d) For which population does the statement "the population grew consistently at million per year" convey accurate information? Why? O A. Population B, because it initially grew slower than population A. O B. Population A, because the average rate of change each year was 100. O C. Population A, because the average growth rate for the four years was 10 OD. Population B, because the average rate of change each year was 100.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![### Population Change Over Time in Two Countries
#### Graph Description
The two curves in the graph describe the numbers of people in two countries as a function of time (t), in years. The population (P), in millions, is plotted against time (t), in years, measured from 0 to 4 years.
- **Population A** is represented by the purple curve.
- **Population B** is represented by the blue curve.
Key data points from the graph:
- Population A starts at (0, 100), reaches (1, 260), dips to (2, 200), then goes up to (3, 300), and finally to (4, 400).
- Population B starts at (0, 100), reaches (1, 100), goes up to (2, 200), then to (3, 150), and finally to (4, 400).
Note: The graph is not drawn to scale.
#### Q&A on Average Growth Rate with Respect to Time
##### (a) Average Growth Rate Calculation
Find the average rate of change of each population with respect to time t as t changes from 0 to 4. This is often called the average growth rate.
- The average growth rate of population A is [_____] million people per year.
- The average growth rate of population B is [_____] million people per year.
##### (b) Growth Pattern Analysis
If the calculation in part (a) were the only one made, would we detect the fact that the populations were growing differently?
- O A. No, the unequal rates suggest similar growth patterns.
- O B. Yes, the unequal rates suggest different growth patterns.
- O C. No, the equal rates suggest similar growth patterns.
- O D. Yes, the equal rates suggest different growth patterns.
##### (c) Average Rate of Change by Year
Find the average rates of change of each population as t changes from:
- 0 to 1
- 1 to 2
- 2 to 3
- 3 to 4
Complete the table with the average rates of change (in millions).
| Population | 0 to 1 | 1 to 2 | 2 to 3 | 3 to 4 |
|------------|--------|--------|--------|--------|
| A | | | | |
| B | | | |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff523dc8a-9051-46da-af12-e46643d993ab%2F07a2a92f-0e1e-4dc3-86e2-f364ec733057%2Fk8xgz8h_processed.png&w=3840&q=75)
Transcribed Image Text:### Population Change Over Time in Two Countries
#### Graph Description
The two curves in the graph describe the numbers of people in two countries as a function of time (t), in years. The population (P), in millions, is plotted against time (t), in years, measured from 0 to 4 years.
- **Population A** is represented by the purple curve.
- **Population B** is represented by the blue curve.
Key data points from the graph:
- Population A starts at (0, 100), reaches (1, 260), dips to (2, 200), then goes up to (3, 300), and finally to (4, 400).
- Population B starts at (0, 100), reaches (1, 100), goes up to (2, 200), then to (3, 150), and finally to (4, 400).
Note: The graph is not drawn to scale.
#### Q&A on Average Growth Rate with Respect to Time
##### (a) Average Growth Rate Calculation
Find the average rate of change of each population with respect to time t as t changes from 0 to 4. This is often called the average growth rate.
- The average growth rate of population A is [_____] million people per year.
- The average growth rate of population B is [_____] million people per year.
##### (b) Growth Pattern Analysis
If the calculation in part (a) were the only one made, would we detect the fact that the populations were growing differently?
- O A. No, the unequal rates suggest similar growth patterns.
- O B. Yes, the unequal rates suggest different growth patterns.
- O C. No, the equal rates suggest similar growth patterns.
- O D. Yes, the equal rates suggest different growth patterns.
##### (c) Average Rate of Change by Year
Find the average rates of change of each population as t changes from:
- 0 to 1
- 1 to 2
- 2 to 3
- 3 to 4
Complete the table with the average rates of change (in millions).
| Population | 0 to 1 | 1 to 2 | 2 to 3 | 3 to 4 |
|------------|--------|--------|--------|--------|
| A | | | | |
| B | | | |
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