Spending on medicare based on the current eligibility

Question

Question: SPENDING ON MEDICARE Based on the current eligibility requirement, a study conducted in 2004 showed that federal spending on entitlement programs, particularly Medicare, would grow enormously in the future. The study predicted that spending on Medicare, as a percentage of the gross domestic product (GDP), will be

P(t) = 0.27t² + 1.4t + 2.2           (0 ≤ t ≤ 5)

percent in year t, where t is measured in decades, with t = 0 corresponding to 2000.

a. How fast will the spending on Medicare, as a percentage of the GDP, be growing in 2010? In 2020?

b. What will the predicted spending on Medicare be in 2010? In 2020?