The two curves below describe the numbers of people in two countries at time t, in years. Answer parts (a) through (d) to the right. Population (in millions) 500- 400- 300- 200- 100- 0 P (1,250) (3,300) (1,100) (2,200), 1 2 3 Time (in years) Note: Graph not drawn to scale. A B (4,400) (3,160) 4 Q 2 a) 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. million people per year. The average growth rate of population A is (Simplify your answer.) The average growth rate of population B is million people per year. (Simplify your answer.) b) 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. OB. Yes, the unequal rates suggest different growth patterns. OC. No, the equal rates suggest similar growth patterns. OD. Yes, the equal rates suggest different growth patterns. c) Find the average rates of change of each population as t changes from 0 to 1; from 1 to 2; from 2 to 3; from 3 to 4. Complete the table with the average rates of change (in millions). A B Population 0 to 1 1 to 2 2 to 3 3 to 4 | |
The two curves below describe the numbers of people in two countries at time t, in years. Answer parts (a) through (d) to the right. Population (in millions) 500- 400- 300- 200- 100- 0 P (1,250) (3,300) (1,100) (2,200), 1 2 3 Time (in years) Note: Graph not drawn to scale. A B (4,400) (3,160) 4 Q 2 a) 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. million people per year. The average growth rate of population A is (Simplify your answer.) The average growth rate of population B is million people per year. (Simplify your answer.) b) 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. OB. Yes, the unequal rates suggest different growth patterns. OC. No, the equal rates suggest similar growth patterns. OD. Yes, the equal rates suggest different growth patterns. c) Find the average rates of change of each population as t changes from 0 to 1; from 1 to 2; from 2 to 3; from 3 to 4. Complete the table with the average rates of change (in millions). A B Population 0 to 1 1 to 2 2 to 3 3 to 4 | |
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question content area left
Part 1
The two curves below describe the numbers of people in two countries at time t, in years. Answer parts (a) through (d) to the right.
nbsp font size decreased by 2 Upper P P
nbsp font size decreased by 2 t t
(1,250) (2,200) (3,160)(4,400)(1,100) (3,300)BA Note: Graph not drawn to scale.
...
Question content area right
Part 1
a) 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
enter your response here
million people per year.(Simplify your answer.)
Part 2
The average growth rate of population B is
enter your response here
million people per year.(Simplify your answer.)
Part 3
b) If the calculation in part (a) were the only one made, would we detect the fact that the populations were growing differently?
No, the unequal rates suggest similar growth patterns.
Yes, the unequal rates suggest different growth patterns.
No, the equal rates suggest similar growth patterns.
Yes, the equal rates suggest different growth patterns.
Part 4
c) Find the average rates of change of each population as t changes from 0 to 1; from 1 to 2; from 2 to 3; from 3 to 4.
Part 5
Complete the table with the average rates of change (in millions).
Part 6
Part 7
Part 8
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Population
|
A
|
B
|
|---|---|---|
|
0 to 1
|
enter your response here
|
enter your response here
|
|
1 to 2
|
enter your response here
|
enter your response here
|
|
2 to 3
|
enter your response here
|
enter your response here
|
|
3 to 4
|
enter your response here
|
enter your response here
|
Part 9
d) For which population does the statement "the population grew consistently at a rate of
100100
million per year" convey accurate information? Why?Population A, because the average growth rate for the four years was
100100.
Population B, because it initially grew slower than population A.
Population B, because the average rate of change each year was
100100.
Population A, because the average rate of change each year was
100100.
Transcribed Image Text:c) Find the average rates of change of each population as t changes from 0 to 1; from 1 to 2;
from 2 to 3; from 3 to 4.
Complete the table with the average rates of change (in millions).
A
B
Population
0 to 1
1 to 2
2 to 3
3 to 4
d) For which population does the statement "the population grew consistently at a rate of 100
million per year" convey accurate information? Why?
O A. Population A, because the average growth rate for the four years was 100.
B. Population B, because it initially grew slower than population A.
O C.
Population B, because the average rate of change each year was 100.
Population A, because the average rate of change each year was 100.
D.
Transcribed Image Text:The two curves below describe the numbers of people in two countries at time t, in years. Answer
parts (a) through (d) to the right.
Population (in millions)
500-
400-
300-
200-
100-
0
P
(1,250)
(3,300)
(1,100)
(2,200),
1
3
2
Time (in years)
Note: Graph not drawn to scale.
A
B
(4,400)
(3,160)
4
Q
Q
C
a) 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.
million people per year.
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 that the
populations were growing differently?
million people per year.
O A. No, the unequal rates suggest similar growth patterns.
B. Yes, the unequal rates suggest different growth patterns.
C. No, the equal rates suggest similar growth patterns.
D. Yes, the equal rates suggest different growth patterns.
c) Find the average rates of change of each population as t changes from 0 to 1; from 1 to 2;
from 2 to 3; from 3 to 4.
Complete the table with the average rates of change (in millions).
A
Population
0 to 1
1 to 2
2 to 3
3 to 4
B
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