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.

4n=2m

ratio of m to n: 2/4 = 1/2

answer

a. 1/2

n+3

step-by-step explanation:

we are increasing our answer by 3 every time. we are moving from negatives to positives, which can make it look confusing, but we are indeed increasing by 3. our next to numbers would be 4, 7, and 10.