Explanation Given information: The amount of smoke (percent of original amount) remaining t minutes after the start of the test is given by, A ( t ) = − 0.00006 t 5 + 0.00468 t 4 − 0.1316 t 3 + 1.915 t 2 − 17.63 t + 100 Calculation: Differentiate the function A ( t ) with respect to t , A ′ ( t ) = d d t ( − 0.00006 t 5 + 0.00468 t 4 − 0.1316 t 3 + 1.915 t 2 − 17.63 t + 100 ) = { d d t ( − 0.00006 t 5 ) + d d t 0.00468 t 4 − d d t 0.1316 t 3 + d d t 1.915 t 2 − d d t 17.63 t + d d t 100 } ( d d x [ f ( x ) ± g ( x ) ] = d d x [ f ( x ) ] ± d d x [ g ( x ) ] ) = { − 0.00006 d d t t 5 + 0.00468 d d t t 4 − 0.1316 d d t t 3 + 1.915 d d t t 2 − 17.63 d d t t + d d t 100 } ( d d x [ c f ( x ) ] = c d d x [ f ( x ) ] ) Simplify it further. A ′ ( t ) = { − 0.00006 ( 5 t 5 − 1 ) + 0.004684 ( 4 t 4 − 1 ) − 0.1316 ( 3 t 3 − 1 ) + 1.915 ( 2 t 2 − 1 ) − 17.63 ( 1 t 1 − 1 ) + 0 } ( d d x ( x ) n = n x n − 1 ) = { − 0.00006 ( 5 t 4 ) + 0.00468 ( 4 t 3 ) − 0.1316 ( 3 t 2 ) + 1.915 ( 2 t ) − 17.63 ( t 0 ) } = − 0.0003 t 4 + 0.01872 t 3 − 0.3948 t 2 + 3.83 t − 17.63 Substitute 10 for t in A ′ ( t ) to find the value of A ′ ( 10 ) . A ′ ( 10 ) = − 0.0003 ( 10 ) 4 + 0.01872 ( 10 ) 3 − 0.3948 ( 10 ) 2 + 3.83 ( 10 ) − 17.63 = − 3 + 18.72 − 39

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 3.5, Problem 39E

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The value of A′(10) , A″(10) , and interpretation of the values.

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Chapter 3.5, Problem 38E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

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The value of A ′ ( 10 ) , A ″ ( 10 ) , and interpretation of the values.

Solution Summary: The author compares the values of Aprime '(10)' and ’a′′' with respect to t.

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The value of A′(10) , A″(10) , and interpretation of the values.

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Chapter 3 Solutions