math
Mr.Q
math.docx窗体顶端
1.5/5 points | Previous AnswersLCalcCon5 1.3.003.
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Graphically estimate the values indicated and answer the question.
(a)
limt → 1− m(t)
2.5
(b)
limt → 1+ m(t)
2.5
(c)
limt → 1m(t)
2.5
(d)
m(1)
3
(e) Is m continuous at t = 1 ? Explain.
Yes. The function m is continuous at t = 1 because the limit exists and is equal to the output value at t = 1.No. The function m is not continuous at t = 1 because even though the limit exists at t = 1 it does not equal the output value of the function for t = 1. No. The function m is not continuous at t = 1 because the limit does not exist at t = 1.No. The function m is not continuous at t = 1 because the left portion of m as t approaches from the left and the right portion of m as t approaches from the right approach different values.No. The function m is not continuous at t = 1 because even though the limit exists, the function is not defined at t = 1.
2.4/4 points | Previous AnswersLCalcCon5 1.3.005.
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Refer to the figure below.
Graphically estimate the values for the function f.
(a)
limx → 6− f(x)
−∞
(b)
limx → 6+ f(x)
−2
(c)
f(6)
−2
(d) Is f continuous at x = 6?
Yes. The function f is continuous at x = 6 because the limit exists and is equal to the output value at x = 6.No. The function f is not continuous at x = 6 because the left portion of f as x approaches 6 from the left and the right portion of f as x approaches 6 from the right approach different values. No. The function f is not continuous at x = 6 because even though the limit exists at x = 6 it does not equal the output value of the function for x = 6.No. The function f is not continuous at x = 6 because even though the limit exists, the function is not defined at x = 6.
3.4/4 points | Previous AnswersLCalcCon5 1.3.007.
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Refer to the figure below.
Graphically estimate the values for the function g.
(a)
limx → 0− g(x)
−3
(b)
limx → 0+ g(x)
−3
(c)
g(0)
−3
(d) Is g continuous at x = 0?
Yes. The function g is continuous at x = 0 because the limit exists and is equal to the output value at x = 0.No. The function g is not continuous at x = 0 because the left portion of g as x approaches 0 from the left and the right portion of g as x approaches 0 from the right approach different values. No. The function g is not continuous at x = 0 because even though the limit exists at x = 0 it does not equal the output value of the function for x = 0.No. The function g is not continuous at x = 0 because the limit does not exist at x = 0.No. The function g is not continuous at x = 0 because even though the limit exists, the function is not defined at x = 0.
4.2/2 points | Previous AnswersLCalcCon5 1.3.009.
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Refer to the figure below.
Assuming the function g continues to follow the same trend shown in the figure for all
x > 4,
graphically estimate the following.
(a)
limx → 8g(x)
12
(b)
limx → ∞ g(x)
∞
5.9/9 points | Previous AnswersLCalcCon5 1.3.011.
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Numerically estimate the limit using a numerical estimation table. Start ±0.1 away from the given input value and estimate the limit to the nearest integer. (If an answer does not exist, enter DNE.)
limx → 2
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1 |
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x − 2 |
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x → 2− |
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x → 2+ |
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1.9 |
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2.1 |
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1.99 |
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2.01 |
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1.999 |
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2.001 |
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1.9999 |
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2.0001 |
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limx → 2
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1 |
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x − 2 |
=
6.–/9 pointsLCalcCon5 1.3.013.
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Numerically estimate the limit using a numerical estimation table. Start ±0.1 away from the given input value and estimate the limit to the nearest integer.
limx → 5
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2x − 10 |
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x − 5 |
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x → 5− |
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x → 5+ |
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4.9 |
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4.99 |
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4.999 |
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5.001 |
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4.9999 |
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5.0001 |
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limx → 5
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2x − 10 |
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x − 5 |
=
7.–/9 pointsLCalcCon5 1.3.015.
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Numerically estimate the limit using a numerical estimation table. Start ±0.1 away from the given input value and estimate the limit to the nearest integer. (Round your table answers to four decimal places.)
limh → 0
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(4 + h)2 − 42 |
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h |
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h → 0− |
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h → 0+ |
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−0.1 |
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0.1 |
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−0.01 |
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0.01 |
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−0.001 |
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0.001 |
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−0.0001 |
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0.0001 |
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limh → 0
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(4 + h)2 − 42 |
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h |
=
8.1/1 points | Previous AnswersLCalcCon5 1.3.017.
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Algebraically determine the limit. (Note: This exercise corresponds to the subsection Algebraically Determining Limits.)
limx → 4 8
9.1/1 points | Previous AnswersLCalcCon5 1.3.019.
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Algebraically determine the limit. (Note: This exercise corresponds to the subsection Algebraically Determining Limits.)
limt → 1 7g(t) when limt → 1 g(t) = 2
10.1/1 points | Previous AnswersLCalcCon5 1.3.027.
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Algebraically determine the limit. (Note: This exercise corresponds to the subsection Algebraically Determining Limits.)
limm → 0
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m |
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m2 + 5m |
11.–/1 pointsLCalcCon5 1.3.031.
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Algebraically determine the limit. (Note: This exercise corresponds to the subsection Algebraically Determining Limits.)
limh → 0
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(4 + h)2 − 42 |
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h |
12.0/4 points | Previous AnswersLCalcCon5 1.3.035.
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Algebraically evaluate the expression and answer the questions. (Note: This exercise corresponds to the subsection Algebraically Determining Limits.)
f(x) =
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8x−1 |
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when x < 4 |
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9x − 34 |
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when x ≥ 4 |
(a)
limx → 4− f(x)
0
(b)
limx → 4+ f(x)
(c)
f(4)
(d) Is f continuous at x = 4?
Yes. The function f is continuous at x = 4 because the limit exists and is equal to the output value at x = 4.No. The function f is not continuous at x = 4 because the left portion of f as x approaches 4 from the left and the right portion of f as x approaches 4 from the right approach different values. No. The function f is not continuous at x = 4 because even though the limit exists at x = 4 it does not equal the output value of the function for x = 4.No. The function f is not continuous at x = 4 because the limit does not exist at x = 4.No. The function f is not continuous at x = 4 because even though the limit exists, the function is not defined at x = 4.
13.6/9 points | Previous AnswersLCalcCon5 2.1.006.
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My Notes
Calculate and write a sentence interpreting each of the following descriptions of change.
For the second quarter of 2009, an airline posted revenue of
$603.6 million
compared with revenue of
$693.1 million
during the second quarter of 2008.
(a) Calculate the change. $ million Interpret.
Between the second quarter of 2008 and the second quarter of 2009, the airline's revenue by $ million.
(b) Calculate the percentage change. (Round your answer to three decimal places.) % Interpret.
Between the second quarter of 2008 and the second quarter of 2009, the airline's revenue by %.
(c) Calculate the average rate of change. $ million per year Interpret.
Between the second quarter of 2008 and the second quarter of 2009, the airline's revenue by an average of $ million per year.
14.5/9 points | Previous AnswersLCalcCon5 2.1.008.
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My Notes
Calculate and write a sentence interpreting each of the following descriptions of change.
The American Indian, Eskimo, and Aleut population in the United States was 362 thousand in 1930 and 4.5 million in 2005.†
(a) Calculate the change. people Interpret.
Between 1930 and 2005, the American Indian population in the United States by people.
(b) Calculate the percentage change. (Round your answer to one decimal place.) % Interpret.
Between 1930 and 2005, the American Indian population in the United States by %.
(c) Calculate the average rate of change. (Round your answer to the nearest integer.) people per year Interpret.
Between 1930 and 2005, the American Indian population in the United States by people per year.
15.3/6 points | Previous AnswersLCalcCon5 2.1.010.
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My Notes
The figure shows the highest elevations above sea level attained by Lake Tahoe (located on the California–Nevada border) from 1982 through 1996.
(a) Draw a secant line connecting the left and right endpoints of the graph. Calculate the slope of this line. (Round your answer to three decimal places.) feet above sea level per year (b) Write a sentence interpreting the slope in the context of Lake Tahoe levels.
Between 1982 and 1996, the level of Lake Tahoe remained fairly constant, by an average of feet above sea level per year.
(c) Write a sentence summarizing how the level of the lake changed from 1982 through 1996. How well does the answer to part (b) describe the change in the lake level as shown in the graph?
The lake level dropped to feet above sea level in 1992 and rose again to a peak of feet above sea level in 1996. The average rate of change between 1982 and 1996 this change in lake level.
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16.6/7 points | Previous AnswersLCalcCon5 2.1.011.
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A graph of a model for the sales of services between 2004 and 2008 by a leading global provider of staffing services is shown below.
(a) Use the graph to calculate the average rate of change in sales of services between 2004 and 2007. $ million per year Interpret the result.
Between 2004 and 2007, sales of service by an average of $ million per year.
(b) Calculate the percentage change in sales between 2007 and 2008. (Round your answer to three decimal places.) % Interpret the result.
Between 2007 and 2008, sales of service by %.
(c) Calculate the change in sales between 2004 and 2008. $ million
17.2/3 points | Previous AnswersLCalcCon5 2.1.012.
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My Notes
The figure shows the median age at first marriage for men in the United States between 1970 and 2007.
(a) Calculate how much and how rapidly the median marriage age increased from 1970 through 2007. (Round your answers to three decimal places.)
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how much |
years |
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how rapidly |
years of age per calendar year |
(b) Did the median age at first marriage for men grow at the same rate from 1970 through 2000 as it did from 2000 through 2007?
YesNo
18.1/3 points | Previous AnswersLCalcCon5 2.1.013.
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My Notes
The table gives the price t, in dollars, of a round-trip flight from Denver to Chicago on a certain airline and the corresponding monthly profit P for that airline on that route.
Round-trip Airfares
|
Ticket Price (dollars) |
Profit (thousand dollars) |
|
200 |
3080 |
|
250 |
3520 |
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300 |
3760 |
|
350 |
3820 |
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400 |
3700 |
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450 |
3380 |
(a) Find the function for the quadratic model that gives the profit in thousand dollars, where t is the ticket price in dollars, with data from
200 ≤ t ≤ 450.
(Round all numerical values to three decimal places.) P(t) =
8.8t+1320
(b) Use the model to calculate the average rate of change of profit when the ticket price rises from $300 to $350. (Round your answer to three decimal places.) thousand dollars per dollar (c) Use the model to calculate the average rate of change of profit when the ticket price rises from $400 to $450. (Round your answer to three decimal places.) thousand dollars per dollar
19.–/4 pointsLCalcCon5 2.1.014.
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My Notes
A travel agent vigorously promotes cruises to Alaska for several months. The table shows the total (cumulative) sales every 3 weeks since the beginning of the special promotion.
Cumulative Sales of Cruise Tickets
|
Week |
Sales to Date (tickets) |
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1 |
71 |
|
4 |
198 |
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7 |
521 |
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10 |
1253 |
|
13 |
2444 |
|
16 |
3660 |
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19 |
4433 |
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22 |
4774 |
|
25 |
4923 |
(a) Find function for the logistic model for cumulative sales, where x is the number of weeks, with data from
1 ≤ x ≤ 25.
(Round all numerical values to three decimal places.)
S(x) ≈
Why is a logistic model appropriate to model these data?
The data are concave down with a relative maximum, which suggests a logistic model.The data are increasing with a constant rate of change, which suggests a logistic model. The data are concave up with a relative minimum, which suggests a logistic model.The data reflect a continual increase and a change in concavity, which suggests a logistic model.The data show a relative maximum and a relative minimum with changes in concavity, which suggests a logistic model.
(b) Calculate the percentage increase in the number of tickets sold between weeks 1 and 16 and between weeks 1 and 25. (Round your answers to one decimal place.)
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between weeks 1 and 16 |
% |
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between weeks 1 and 25 |
% |
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20.2/5 points | Previous AnswersLCalcCon5 2.1.015.
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My Notes
The life expectancies of black males in the United States at various ages for 2006 are as shown below.
Life Expectancy of Black Males by Age
|
Age (years) |
Life Expectancy (years) |
|
At birth |
69.7 |
|
10 |
60.9 |
|
20 |
51.3 |
|
30 |
42.4 |
|
40 |
33.5 |
|
50 |
25.2 |
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60 |
18.2 |
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70 |
12.3 |
(a) How rapidly, on average, does the life expectancy change between birth and the 70th year of life for black males in the United States? (Round your answer to two decimal places.) years per year (b) Compare the average rates of change of life expectancy for the 10-year periods between ages 40 and 50 and ages 50 and 60. (Round your answers to two decimal places.)
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between ages 40 and50 |
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between ages 50 and60 |
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Life expectancy decreases more rapidly between ages than between ages .
21.1/3 points | Previous AnswersLCalcCon5 2.1.017.
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My Notes
The number of Internet users in Mexico between 2004 and 2008 can be modeled as
u(t) = 8.02(1.17t) million users
where t is the number of years since 2004.†
(a) On average, what was the rate of change in the number of Internet users in Mexico between 2004 and 2006? (Round your answer to three decimal places.) million users per year (b) What was the percentage change in the number of Internet users in Mexico between 2004 and 2006? (Round your answer to three decimal places.) % (c) The population of Mexico in 2008 was 109,955,400. What percentage of the Mexican population used the Internet in 2008? (Round your answer to three decimal places.) %
22.–/4 pointsLCalcCon5 2.1.018.
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My Notes
The number of AIDS cases diagnosed from 2000 through 2007 can be modeled as
f(x) = 3.23(1.06x) hundred thousand cases
where x is the number of years since 2000.†
(a) Calculate the average rate of change in the number of persons diagnosed with AIDS between 2000 and 2007. (Round your answer to three decimal places.) hundred thousand cases per year. Write a sentence of interpretation.
Between 2000 and 2007, the number of AIDS cases diagnosed by cases per year.
(b) Calculate the percentage change in the number of persons diagnosed with AIDS between 2000 and 2007. (Round your answer to three decimal places.) %
23.–/3 pointsLCalcCon5 2.1.019.
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My Notes
99.2% of ATMs levy a surcharge on users who are not account holders. The amount of the surcharge for non-account holders can be modeled as
s(t) = 0.72(1.081t) dollars
where t is the number of years since 1995, data from 3 ≤ t ≤ 13.†
(a) Calculate the average rate of change in the amount of the surcharge for non-account holders between 2001 and 2006. Write the result in a sentence of interpretation. (Round your answer to two decimal places.)
Between 2001 and 2006, the ATM surcharge for non account holders increased by an average of $ per year.
(b) Calculate the change and the percentage change in the amount of the surcharge for non-account holders between 2001 and 2006. (Round your answers to two decimal places.)
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change |
$ |
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percentage change |
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% |
24.–/8 pointsLCalcCon5 2.1.021.
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My Notes
For the linear function answer the following.
f(x) = 9x + 2
(a) Calculate the average rate of change and the percentage change in f for each of the following intervals. (Round your answers to three decimal places.)
i. From
x = 1
to
x = 3
|
average rate of change |
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percent change |
% |
ii. From
x = 3
to
x = 5
|
average rate of change |
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percent change |
% |
iii. From
x = 5
to
x = 7
|
average rate of change |
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percent change |
% |
(b) On the basis of the results in part (a) and the characteristics of linear functions presented in Chapter 1, what generalizations can be made about percentage change and average rate of change for a linear function?
For a linear function, the average rate of change between two points , but the percentage change .
25.–/8 pointsLCalcCon5 2.1.022.
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My Notes
For the exponential function answer the following.
f(x) = 8(0.9x)
(a) Calculate the percentage change and average rate of change of f for each of the following intervals. (Round your answer to three decimal places.)
i. From
x = 1
to
x = 3
|
average rate of change |
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percent change |
% |
ii. From
x = 3
to
x = 5
|
average rate of change |
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percent change |
% |
iii. From
x = 5
to
x = 7
|
average rate of change |
|
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percent change |
% |
(b) On the basis of the results in part (a) and the characteristics of exponential functions presented in Chapter 1, what generalizations can be made about percentage change and average rate of change for an exponential function?
For an exponential function, the average rate of change between two points , but the percent change .
26.–/7 pointsLCalcCon5 2.1.024.
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My Notes
The cesarean delivery rate jumped 27.5% between 2001 and 2006 and 2.6% between 2005 and 2006.
(a) If the cesarean delivery rate was 31.1 per 100 live births in 2006, calculate the cesarean delivery rates in 2001 and 2005. (Round your answer to three decimal places.)
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cesarean delivery rates in 2001 |
per 100 live births |
|
cesarean delivery rates in 2005 |
per 100 live births |
(b) Use the information presented in the table to find a model for the cesarean delivery rate between 2000 and 2008, where x is the number of years since 2000. (Round numerical values to three decimal places.)
f(x) =
Cesarean Delivery Rate (cesarean deliveries per 100 live births)
|
Year |
Cesarean Deliveries (per 100 live births) |
|
2000 |
22.9 |
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2002 |
26.1 |
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2004 |
29.1 |
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2006 |
31.1 |
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2008 |
32.5 |
(c) Use the model to calculate the cesarean delivery rates in 2001 and 2005. (Round your answers to three decimal places.)
|
cesarean delivery rates in 2001 |
per 100 live births |
|
cesarean delivery rates in 2005 |
per 100 live births |
How close are those values to the results of part (a)?
This answer has not been graded yet.
Are these estimates found with interpolation or extrapolation?
extrapolationinterpolation
窗体底端
14
1/5
89.5
decreased
12.913
decreased
decreased
4138000
increased
4138000
114.3
increased
55174
55174
0.11
increasing
6221.87
6229.09
fails to describe
274
increased
1.691
1.691
731
4.4
1.1
1.2
6.4
463.2
683.4
0.82
0.83
0.7
40 and 50
S
ubmit Answer
50 and 60
0.798
17
13.668
S
ave Progress
S
ave Progress
-10
10
-100
100
-1000
1000
-10000
10000
DNE
8
