National health care national expenditures for health care H (in billions of dollars) have risen dramatically in the past 20 years.

By using U.S. Department of Health and Human Services, Center for Medicare and Medicaid Services data from 2000 and projected to 2015, the rate of change of expenditures can be modeled by

dH/dt = 10.666t + 100.5

billions of dollars per year, where t = 0 represents 2000.

(a) Find the function that models the national expenditures for health care if expenditures in 2009 were $2689 billion.

(b) Use the model from part (a) to predict the national health care expenditures for 2015.