Explanation Given: Initial reading of the thermometer is 70 ° F which is placed in a pre-heated oven. The given conditions regarding the temperature of the thermometer are T ( 1 2 ) = 110 ° F and T ( 1 ) = 145 ° F . Calculation: Consider the equation for the Newton’s law of warming. T ( t ) = T m + c e k t (1) Here, T ( t ) is the temperature of the thermometer, T m is temperature of the oven and k is the constant. Substitute 0 for t and T ( 0 ) = 70 ° F in equation (1). T ( 0 ) = T m + c e k ( 0 ) 70 = T m + c c = 70 − T m Substitute 70 − T m for c in equation (1). T ( t ) = T m + ( 70 − T m ) e k t (2) Substitute 1 2 for t and T ( 1 2 ) = 110 ° F in equation (2). T ( 1 2 ) = T m + ( 70 − T m ) e k ( 1 2 ) 110 = T m + ( 70 − T m ) e k 2 e k 2 = 110 − T m 70 − T m (3) Substitute 1 for t and T ( 1 ) = 145 ° F in equation (2)

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 2.7, Problem 17E

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Calculate the temperature of the oven.

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Calculate the temperature of the oven.

Solution Summary: The author calculates the temperature of the oven using the Newton's law of warming equation.

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