(a) Explanation Given information: The projected number of nurses (in millions) in year t from 2000 through 2015 is given by, N ( t ) = { 1.9 if 0 ≤ t < 5 − 0.0004 t 2 + 0.038 t + 1.72 if 5 ≤ t ≤ 15 The projected number of nursing jobs (in millions) over the same periods is given by, J ( t ) = { − 0.0002 t 2 + 0.032 t + 2 if 0 ≤ t < 10 − 0.0016 t 2 + 0.12 t + 1.26 if 10 ≤ t ≤ 15 Here, t = 0 corresponds to year 2000. Calculation: Function G is the difference of both the functions. Divide the time period into three parts. For 0 ≤ t < 5 , the function G is, G = J − N G ( t ) = J ( t ) − N ( t ) = − 0.0002 t 2 + 0.032 t + 2 − 1.9 = − 0.0002 t 2 + 0.032 t + 0.1 For 5 ≤ t < 10 , the function G is, G = J − N G ( t ) = J ( t ) − N ( t ) = − 0 (b) To determine The rate of change of gap between demand and supply of nurses in 2008 and 2012.

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Question

Chapter 3.1, Problem 75E

(a)

To determine

The rule for the function G=J−N which gives the supply and the demand of nurses from 2000 through 2015.

(b)

To determine

The rate of change of gap between demand and supply of nurses in 2008 and 2012.

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Chapter 3.1, Problem 74E

Chapter 3.1, Problem 76E

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Applied Calculus for the Managerial, Life, and Social Sciences

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The rule for the function G = J − N which gives the supply and the demand of nurses from 2000 through 2015.

Solution Summary: The author explains the rule for the function G=J-N which gives the supply and demand of nurses from 2000 through 2015. The projected number of nursing jobs is given by, J(t)=