a. Explanation Given information: The temperature of the casserole will cool by changing at a rate of T ' ( t ) = − 15 e − 0.5 t degrees Fahrenheit temperature. Formula used : ∫ e a x d x = e a x a + C Calculation: T ' ( t ) = − 15 e − 0.5 t (Given) ∫ T ' ( t ) d t = ∫ − 15 e − 0.5 t d t = − 15 ∫ e − 0.5 t d t = − 15 ( e − 0.5 t − 0.5 ) + C = 30 e − 0.5 t + C Thus , T ( t ) = ∫ T ' ( t ) d t = 30 e − 0 b. To determine To calculate : T ( 5 ) − T ( 0 ) and to write the connection between Riemann sums and antidifferentiation.

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Differential Equations

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Question

Chapter 4.4, Problem 70A

To determine

To calculate: ∫T'(t)dt and the formula for the temperature T(t) of the casserole after t minutes with the given T0=350 degrees.

To determine

To calculate: T(5)−T(0) and to write the connection between Riemann sums and antidifferentiation.

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Chapter 4.4, Problem 69A

Chapter 4.4, Problem 71P

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∫ T ' ( t ) d t and the formula for the temperature T ( t ) of the casserole after t minutes with the given T 0 = 350 degrees.

Solution Summary: The author calculates the temperature of the casserole after t minutes with the given T_0=350 degrees.