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
$$
P(t)=0.27 t^{2}+1.4 t+2.2 \quad(0 \leq t \leq 5)
$$
percent in year $t,$ where $t$ is measured in decades, with $t=0$ corresponding to $2000 .$
a. How fast was the spending on Medicare, as a percentage of the GDP, growing in $2010 ?$ How fast will it be growing in $2020 ?$
b. What was the predicted spending on Medicare in $2010 ?$ What will it be in $2020 ?$
Source: Congressional Budget Office.