Explanation Given: The level of formaldehyde in an average home is, f ( t ) = 0.055 t + 0.26 t + 2 (1) Where, ( 0 ≤ t ≤ 12 ) and the value of t corresponds to the age of the house in years. Formula used: The quotient rule to differentiate the function f ( x ) = g ( x ) h ( x ) , where h ( x ) ≠ 0 is, d d x ( f ( x ) ) = d d x ( g ( x ) h ( x ) ) = h ( x ) d d x ( g ( x ) ) − g ( x ) d d x ( h ( x ) ) ( h ( x ) ) 2 Calculation: Use quotient rule to differentiate both side of the equation (1) with respect to t, to get the rate of change of level of formaldehyde of the average house dropping. d d t ( f ( t ) ) = d d t ( 0.055 t + 0.26 t + 2 ) f ′ ( t ) = ( t + 2 ) d d t ( 0.055 t + 0.26 ) − ( 0.055 t + 0.26 ) d d t ( t + 2 ) ( t + 2 ) 2 = ( t + 2 ) ( 0.055 + 0 ) − ( 0.055 t + 0.26 ) ( 1 + 0 ) ( t + 2 ) 2 = 0

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 3.2, Problem 63E

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To find: The rate of change of level of formaldehyde of the average house when it is new and at the beginning of the fourth year.

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Chapter 3.2, Problem 62E

Chapter 3.2, Problem 65E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The rate of change of level of formaldehyde of the average house when it is new and at the beginning of the fourth year.

Solution Summary: The author calculates the rate of change of level of formaldehyde in an average house when it is new and at the beginning of the fourth year.

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Chapter 3 Solutions