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Air conditioning is turned off in an empty building. Initially, at 6PM, it has an interior temperature of 60°F. The building has a time constant of 4 hours. (Note: This is the time constant, not the constant of proportionality in Newton's Law.) The outdoor temperature fluctuates sinusoidally, reaching a maxmimum of 100°F at noon and a minimum of 60°F at midnight every day. Assume there are no heating or cooling effects on the build aside from Newton's Law of Cooling. Model the building's temperature as a function of time.

Air conditioning is turned off in an empty building. Initially, at 6PM, it has an interior temperature of 60°F. The building has a time constant of 4 hours. (Note: This is the time constant, not the constant of proportionality in Newton's Law.) The outdoor temperature fluctuates sinusoidally, reaching a maxmimum of 100°F at noon and a minimum of 60°F at midnight every day. Assume there are no heating or cooling effects on the build aside from Newton's Law of Cooling. Model the building's temperature as a function of time.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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2. For each of the situations described below, use an initial value problem to model the situation. Clearly define any variables and functions used. Do not solve the initial value problems.
Transcribed Image Text:2. For each of the situations described below, use an initial value problem to model the situation. Clearly define any variables and functions used. Do not solve the initial value problems.
b. Air conditioning is turned off in an empty building. Initially, at 6PM, it has an interior temperature of 60°F. The building has a time constant of 4 hours. (Note: This is the time constant, not the constant of proportionality in Newton's Law.) The outdoor temperature fluctuates sinusoidally, reaching a maxmimum of 100°F at noon and a minimum of 60°F at midnight every day. Assume there are no heating or cooling effects on the build aside from Newton's Law of Cooling. Model the building's temperature as a function of time.
Transcribed Image Text:b. Air conditioning is turned off in an empty building. Initially, at 6PM, it has an interior temperature of 60°F. The building has a time constant of 4 hours. (Note: This is the time constant, not the constant of proportionality in Newton's Law.) The outdoor temperature fluctuates sinusoidally, reaching a maxmimum of 100°F at noon and a minimum of 60°F at midnight every day. Assume there are no heating or cooling effects on the build aside from Newton's Law of Cooling. Model the building's temperature as a function of time.
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