a. Explanation Given Information: Rate of change of casserole temperature given by T ( t ) = − 15 e − 0.5 t For the given time t = 0 , 1 , 2 , 3 , 4 , 5 . Time t ( min ) 0 1 2 3 4 5 T(t)(degree) -15 -9.1 -5.5 -3.3 -2.03 -1.23 The given function T ′ ( t ) on the rate of change of the temperature is decreasing over the given time b. To determine To Explain : the change in the temperature T can be approximated by the area under the graph of T ′ ( t ) c. To determine To Find: the change in the temperature over first five minutes using Riemann sum approximation n=4

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Differential Equations

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Chapter 4.2, Problem 47A

To determine

To Explain: the behavior of the graph of T′(t)

To determine

To Explain: the change in the temperature T can be approximated by the area under the graph of T′(t)

To determine

To Find: the change in the temperature over first five minutes using Riemann sum approximation n=4

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Chapter 4.2, Problem 46A

Chapter 4.2, Problem 48A

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Calculus

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the behavior of the graph of T ′ ( t )

Solution Summary: The author explains the behavior of the graph of T′(t) 0 is decreasing. The area under the curve is time multiplied by the velocity equals the distance.

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To Explain: the behavior of the graph of T′(t)

To Explain: the change in the temperature T can be approximated by the area under the graph of T′(t)

To Find: the change in the temperature over first five minutes using Riemann sum approximation n=4

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Chapter 4 Solutions