(a) Explanation Given information: The spending on Medicare, as a percentage of the gross domestic product (GDP) is, P ( t ) = 0.27 t 2 + 1.4 t + 2.2 Here, t is measured in decades, t = 0 corresponds to 2000, and 0 ≤ t ≤ 5 . Calculation: The rate of change of spending on Medicare is the derivative of the function P ( t ) = 0.27 t 2 + 1.4 t + 2.2 . Differentiate the function P ( t ) with respect to t , P ′ ( t ) = d d t ( 0.27 t 2 + 1.4 t + 2.2 ) = d d t 0.27 t 2 + d d t 1.4 t + d d t 2.2 ( d d x [ f ( x ) ± g ( x ) ] = d d x [ f ( x ) ] ± d d x [ g ( x ) ] ) = 0.27 d d t t 2 + 1.4 d d t t + d d t 2.2 ( d d x [ c f ( x ) ] = c d d x [ f ( x ) ] ) = 0.27 ( 2 t 2 − 1 ) + 1 (b) To determine The predicted spending on Medicare in year 2010 and 2020.

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 3.1, Problem 62E

(a)

To determine

The rate of change of spending on Medicare in 2010 and 2020.

(b)

To determine

The predicted spending on Medicare in year 2010 and 2020.

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Chapter 3.1, Problem 61E

Chapter 3.1, Problem 63E

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Chapter 3 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

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The rate of change of spending on Medicare in 2010 and 2020.

Solution Summary: The author calculates the rate of change of spending on Medicare, as a percentage of the gross domestic product (GDP).

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The rate of change of spending on Medicare in 2010 and 2020.

The predicted spending on Medicare in year 2010 and 2020.

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