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) = 0.27t^2 + 1.4t + 2.2 (0 ? t ? 5) percent in year t, where t is measured in decades, with t = 0 corresponding to 2000. (Round your answers to two decimal places.) (a) How fast was the spending on Medicare, as a percentage of the GDP, growing in 2020? %/decade How fast will it be growing in 2040? %/decade (b) What was the predicted spending on Medicare in 2020? % What will it be in 2040? %
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Given: \[ P(t) = 0.27t^2 + 1.4t + 2.2 \] Differentiate \( P(t) \) with respect to \( t \): \[ P'(t) = 0.54t + 1.4 \] Calculate the rate of growth in 2020 (when \( t = 2 \)): \[ P'(2) = 0.54(2) + 1.4 = 2.4\% \text{ per decade} \] ** Show more…
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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) = 0.27t^2 + 1.4t + 2.2 (0 ≤ t ≤ 5) percent in year t, where t is measured in decades, with t = 0 corresponding to 2000. (Round your answers to two decimal places.) (a) How fast was the spending on Medicare, as a percentage of the GDP, growing in 2020? %/decade How fast will it be growing in 2050? %/decade (b) What was the predicted spending on Medicare in 2020? % What will it be in 2050? %
Eduard S.
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) = 0.27t^2 + 1.4t + 2.2 (0 ≤ t ≤ 5) percent in year t, where t is measured in decades, with t = 0 corresponding to 2000.† (Round your answers to two decimal places.) (a) How fast was the spending on Medicare, as a percentage of the GDP, growing in 2020? How fast will it be growing in 2040? (b) What was the predicted spending on Medicare in 2020? What will it be in 2040?
Qbs E.
Aging baby boomers will put a strain on Social Security benefits unless Congress takes action. The Social Security benefits to be paid out from 2010 through 2040 are projected to be $$S(t)=0.1375 t^{2}+0.5185 t+0.72 \quad(0 \leq t \leq 3)$$ where $S(t)$ is measured in trillions of dollars and $t$ is measured in decades, with $t=0$ corresponding to 2010. a. What was the amount of Social Security benefits paid out in $2010 ?$ b. What is the amount of Social Security benefits projected to be paid out in $2040 ?$
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