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um122431

um122431

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Central University of Gujarat - CUG

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Algebra3
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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.
 
 
 
Answer: (a) Write the equation using the values on calculator. Report the mode...
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