   Chapter 12.3, Problem 50E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Temperature changes When an object is moved from one environment to another, its temperature T changes at a rate given by d T d t = k C e k t where t is the time in the new environment (in hours), C is the temperature difference (old - new) between the two environments, and k is a constant. If the temperature of the object (and the old environment) is 70°F and C = - 10°F , what function describes the temperature T of the object t hours after it is moved?

To determine

To calculate: The function that describe the temperature T of the object t hours after it is moved when the temperature T changes at a rate given by dTdt=kCekt; where t is the time in the new environment, C is the temperature difference between the two environment and k is a constant.

Explanation

Given Information:

When the object is moved from one environment to another, its temperature T changes at a rate given by

dTdt=kCekt

Where t is the time in the new environment, C is the temperature difference between the two environment, and k is a constant.

If the temperature of the object is 70F and C=10F.

Formula used:

If u is a function of x, then euudx=eudu=eu+C

Calculation:

Rewrite dTdt=kCekt as dT=kCektdt

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