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25 Aug 2022
First photo is the main question. And example is on the second photo.
The table shows the national expenditures for health care (in billions of dollars) for selected years from 2002 and projected to 2024 . (These data include expenditures for medical research and medical facilities construction.)
Complete parts (a) through (c) below.
Year
Expenditures
Year
Expenditures
2002
1601
2014
3081
2004
1856
2016
3403
2006
2114
2018
3786
2008
2414
2020
4274
2010
2605
2022
4826
2012
2818
2024
5426
a. Find a linear function that models the data, with x equal to the number of years after 2000 and y equal to the expenditures for health care in billions of dollars. Report the model with 3 significant digits.
y= ____x + ____
b. What does the reported model predict the expenditures will be in 2030?
$ ___ billion (Use the answer from a to find this answer.)
c. During what year does the reported model predict that the national expenditures for health care will be $ 7906 billion?
The reported model predicts that the national expenditures for health care will be $ 7906 billion in the year ____
(Use the answer from a to find this answer.)
The table shows the national expenditures for heath care (in billions of dollars) for selected years from 2002 and projected to 2024. (These data include expenditures for medical research and medical facilities construction)
Complete parts (a) through (c) below.
Year
Expenditures
Year
Expenditures
2002
1603
2014
3082
2004
1855
2016
3403
2006
2113
2018
3787
2008
2415
2020
4275
2010
2606
2022
4824
2012
2817
2024
5425
a. Find a linear function that models the data, with x equal to the number of years after 2000 and y equal to the expenditures for health care in billons of dollars. Report the model with 3 significant digits.
Use the table below to find the linear function.
x 2 4 6 8 10 12 14 16 18 20 22 24
y 1603 1855 2113 2415 2606 2817 3082 3403 3787 4275 4824 5425
Enter the data into a calculator and use the linear regression function to model the data. The function will display the coefficients, a and b, of a linear equation y=ax + b.
Write the equation using the values on the graphing calculator. Report the model with 3 significant digits.
y=163 x+1060
Therefore, a linear model for the data in the table is y=163 x+1060.
What does the reported model predict the expenditures will be in 2040 ?
Find the x-value that corresponds to the given year, and substitute it for x in the model. The x-value that corresponds to 2040 is 40 .
Now substitute 40 for x in the model and simplify, rounding to three decimal places.
y = 163x + 1060
= 163(40) + 1060
= 6520 + 1060 Multiply
= 7580 Add
Thus, there will be about $ 7580 billon expenditures in 2040.
c. During what year does the reported model predict that the national expenditures for health care will be $ 8395 billion?
To find this, substitute 8395 for y in the model and solve for x
Now substitute 8395 for y in the model.
y = 163x + 1060
8395 = 163x + 1060
8395 - 1060 = 163x +1060-1060 Subtract 1060 from both sides.
7335 = 163x Simplify
Now isolate x, rounding to the nearest whole number.
First photo is the main question. And example is on the second photo.
The table shows the national expenditures for health care (in billions of dollars) for selected years from 2002 and projected to 2024 . (These data include expenditures for medical research and medical facilities construction.)
Complete parts (a) through (c) below.
Year | Expenditures | Year | Expenditures |
2002 | 1601 | 2014 | 3081 |
2004 | 1856 | 2016 | 3403 |
2006 | 2114 | 2018 | 3786 |
2008 | 2414 | 2020 | 4274 |
2010 | 2605 | 2022 | 4826 |
2012 | 2818 | 2024 | 5426 |
a. Find a linear function that models the data, with x equal to the number of years after 2000 and y equal to the expenditures for health care in billions of dollars. Report the model with 3 significant digits.
y= ____x + ____
b. What does the reported model predict the expenditures will be in 2030?
$ ___ billion (Use the answer from a to find this answer.)
c. During what year does the reported model predict that the national expenditures for health care will be $ 7906 billion?
The reported model predicts that the national expenditures for health care will be $ 7906 billion in the year ____
(Use the answer from a to find this answer.)
The table shows the national expenditures for heath care (in billions of dollars) for selected years from 2002 and projected to 2024. (These data include expenditures for medical research and medical facilities construction)
Complete parts (a) through (c) below.
Year | Expenditures | Year | Expenditures |
2002 | 1603 | 2014 | 3082 |
2004 | 1855 | 2016 | 3403 |
2006 | 2113 | 2018 | 3787 |
2008 | 2415 | 2020 | 4275 |
2010 | 2606 | 2022 | 4824 |
2012 | 2817 | 2024 | 5425 |
a. Find a linear function that models the data, with x equal to the number of years after 2000 and y equal to the expenditures for health care in billons of dollars. Report the model with 3 significant digits.
Use the table below to find the linear function.
x 2 4 6 8 10 12 14 16 18 20 22 24
y 1603 1855 2113 2415 2606 2817 3082 3403 3787 4275 4824 5425
Enter the data into a calculator and use the linear regression function to model the data. The function will display the coefficients, a and b, of a linear equation y=ax + b.
Write the equation using the values on the graphing calculator. Report the model with 3 significant digits.
y=163 x+1060
Therefore, a linear model for the data in the table is y=163 x+1060.
What does the reported model predict the expenditures will be in 2040 ?
Find the x-value that corresponds to the given year, and substitute it for x in the model. The x-value that corresponds to 2040 is 40 .
Now substitute 40 for x in the model and simplify, rounding to three decimal places.
y = 163x + 1060
= 163(40) + 1060
= 6520 + 1060 Multiply
= 7580 Add
Thus, there will be about $ 7580 billon expenditures in 2040.
c. During what year does the reported model predict that the national expenditures for health care will be $ 8395 billion?
To find this, substitute 8395 for y in the model and solve for x
Now substitute 8395 for y in the model.
y = 163x + 1060
8395 = 163x + 1060
8395 - 1060 = 163x +1060-1060 Subtract 1060 from both sides.
7335 = 163x Simplify
Now isolate x, rounding to the nearest whole number.
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adityaag1507Lv10
26 Aug 2022
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