Write H(t) for the amount 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)

H'(t) = ? billion dollars per yr

(b) Given that $1,300 billion was spent on health care in the United States in 2000, find the function H(t).

H(t) = ? billion dollars

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.

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