Question

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. Find a linear model for the rate of change H'(t)

Answer 1

Answer: Linear model
`H(t)=9t+100` and H'(t) = 9 units.

Explanation:

Since we have given that

In 2000, amount spent = $100 billions

In 2010, amount spent = $190 billions.

So, rate of increase would be

`(190-100)/(2010-2000)\\\\=(90)/(10)\\\\=9`

So, linear model for H(t) would be

`H(t)-190=9(t-10)\\\\H(t)=9t-90+190\\\\H(t)=9t+100`

So, H'(t) would be 9.

Hence, linear model
`H(t)=9t+100` and H'(t) = 9 units.