Answer:
Check the explanation
Step-by-step explanation:
Write H(t) for the total sum spent in the United States on health care in year t, where t is measured in years since 2000.
The rate of increase of H(t) was projected to rise from $100 billion per year in 2000 to approximately $190 billion per year in 2010
(a) Find a linear model for the rate of change H'(t)
Slope of line is (190-100)/(2010-2000) = 90/10 = 9 billion dollars per yr
H'(t) - 190 = 9 (t-10) =
H'(t) = 9t + 100 billions dollars per year
(b) Given that $1,300 billion was spent on health care in the United States in 2000, find the function H(t).
H'(t) = 9t + 100 billions dollars per year TAKING INTEGRATION..
H(t) = 9t^2/2 + 100t + C given H(0) = 1300
H(0) = 1300 = C
H(t) = 9t^2/2 + 100t + 1300 billion dollars.