Question

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? %

          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?
%

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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?
%

Added by -Ngel E.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Eduard Sanchez

02/10/2023

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In 2020, the predicted spending on Medicare, percentage of the GDP, 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? %

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00:01 Hi there, so for this problem, the expression that we're given for the percentage of the gross domestic product, p .gdp, is given by the following expression that will be 0 .27 times the time squared plus 1 .4 times the time plus 2 .2.

00:22 Okay.

00:23 Now, this and the time equals to 0 corresponds to the year 2 ,000, okay? so the first question for part a of this problem is how fast was the spending on medicare as a percentage of the gdp growing in 2010? so the amount of years since 2000 is 20 years, then we just need first to take the derivative of this expression with respect to time.

00:50 So that will be 0 .27 times 2.

00:54 So we will have 0 .54 this times a time plus 1 .1 .4 .5 .5 .5.

01:00 And now we just need to evaluate this at 20.

01:05 So that will be 0 .54 times 20 and this plus 1 .4.

01:11 Then using our calculator, we obtain a value of 12 .2 % in this per decade.

01:27 So that's a solution for part now, oh sorry, the time is measured in decades.

01:39 Okay, so i have made a mistake in here, okay? so because 2020 corresponds to two decades later of 2000.

01:50 So that will be that the time is two, so please fit that in there.

01:53 So that will be 0 .54 times 2 and this plus 1 .4.

01:59 So the current solution for this, let me fit that in here.

02:03 That will be 2 .48 in units of percentage per decade.

02:11 Okay...

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