Solve the Problem $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}+19 \mathrm{x}+293$ , Where $x$ Represents the Number of Years After 1995

Solve the problem.
-The amount of money, in billions of dollars, spent on health care that was covered by insurance in a certain country in a particular year can be approximated by the function $\mathrm{f}(\mathrm{x}) =\mathrm{x}^{2}+19 \mathrm{x}+293$ , where $x$ represents the number of years after 1995. The amount of money, in billions of dollars, spent on health care that was paid out of pocket in a certain country in a particular year can be approximated by the function $\mathrm{g}(\mathrm{x}) =5 \mathrm{x}+142$ , where again $\mathrm{x}$ represents the number of years after 1995.
(i) Find ( $\mathrm{f}-\mathrm{g}) (\mathrm{x})$ . Explain, in your own words, what this function represents.
(ii) Find ( $\mathrm{f}-\mathrm{g}) (55)$ . Explain, in your own words, what this number represents.

A) (i) ( $\mathrm{f}-\mathrm{g}) (\mathrm{x}) =\mathrm{x}^{2}+14 \mathrm{x}+151$ ; this is the difference between health- care costs covered by insurance and health- care costs that are paid out of pocket, in billions of dollars, $x$ years after 1995.
(ii) 3946; health- care costs covered by insurance will be $\$ 3,946,000,000,000$ higher than health- care costs that are paid out of pocket in 2050.
B) (i) (f - g) $(x) =x^{2}-24 x-435$ ; this is the difference between health- care costs covered by insurance and health- care costs that are paid out of pocket, in billions of dollars, $\mathrm{x}$ years after 1995.
(ii) 1270; health- care costs covered by insurance will be $\$ 1,270,000,000,000$ higher than health- care costs that are paid out of pocket in 2050.
C) (i) (f - g) (x) $=x^{2}-24 x-435$ ; this is the difference between health- care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, $\mathrm{x}$ years after 1995.
(ii) 1270; health- care costs covered by insurance will be $\$ 1,270,000,000,000$ less than heal th- care costs that are paid out of pocket in 2050.
D) (i) (f - g) $(x) =x^{2}+14 x+151$ ; this is the difference between health- care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, $\mathrm{x}$ years after 1995.
(ii) 3946; health- care costs covered by insurance will be $\$ 3,946,000,000,000$ less than heal th- care costs that are paid out of pocket in 2050.