Answer
a. $5.48+0.04x=y$
b. $1.84+0.17x=y$
c. $2028$, $y=6.6$, Medicare
Work Step by Step
The function that models the cost of Social Security as a percentage of the GDP $x$ years after $2000$ is the initial social security cost as a percentage of the GDP plus the rate at which it is increasing times the year.
a. $5.48+0.04x=y$
The function that models the cost of Medicare as a percentage of the GDP $x$ years after $2000$ is the initial Medicare cost as a percentage of the GDP plus the rate at which it is increasing times the year.
b. $1.84+0.17x=y$
c. The cost of Medicare as a percentage of GDP equals the cost of Social Security as a percentage of GDP means that the $y$ is equal.
Therefore,
.$5.48+0.04x=1.84+0.17x$,
$5.48-1.84=0.17x-0.04x$,
$3.64=0.13x$,
$x=28^{th} year$ after $2000$
$2000+28=2028$ Medicare will have a the same cost as Social Security.
$y=1.84+0.17(28)=6.6$
After $2028$, Medicare will have a greater cost.
