The projected amount the average American spent on health care in 2014 is $ 10075.91
Solution:
Given that,
The average American spent $8,508 on health care in 2011
The cost of health care is projected to rise about 5.8% per year for the years 2012-2022
The increasing function is given as:
[tex]y = a(1+r)^t[/tex]
Where,
y is future value
a is initial value
r is growth rate in decimal
t is number of years
From given,
a = 8508
[tex]r = 5.8 \% = \frac{5.8}{100} = 0.058[/tex]
t = 2011 to 2014 = 3 years
Substituting the values, we get,
[tex]y = 8508(1 + 0.058)^3\\\\y = 8508(1.058)^3\\\\y = 8508 \times 1.1842\\\\y = 10075.914 \approx 10075.91[/tex]
Thus the projected amount the average American spent on health care in 2014 is $ 10075.91
