Using U.S. Centers for Medicare and Medicaid Services data from 2000 and projected to 2024, the total U.S. expenditures (in billions of dollars) for professional health services and retail medical products (including
prescription drugs) can be modeled by

y = 617e^0.0505t

where t is the number of years after 2000.

(a) Find the function that models the rate of change.

(b) Find the model’s value for the rate of change of U.S. expenditures for professional health services and retail medical products in 2010 and in 2020.