1. With U.S. Department of Health and Human Services data from 2000 and projected to 2018, the total public expenditures for health care H can be modeled by
H = 624e0.07t
where t is the number of years past 2000 and H is in billions of dollars. If this model is accurate, at what rate will health care expenditures change in 2020?
2. By using U.S. Bureau of Labor Statistics data for selected years from 1988 and projected to 2018, the billions of dollars spent for personal consumption in the United States can be modeled by
P = 2969e0.051t
where t is the number of years past 1985. If this model is accurate, find and interpret the rate of change of personal consumption in 2015.
3. The intensity of an earthquake is related to the Richter scale reading R by
I / I0 = 10R
where I0 is a standard minimum intensity. If I0 = 1, what is the rate of change of the intensity I with respect to the Richter scale reading?