II: Exponential Decay: Newton's Law of Cooling An object at 80° C is in an environment where the temperature is a constant 25° C. (The environment is large enough that the cooling object does not raise the temperature of its surroundings. T₁ surrowing Her To Hory of Tlol: Ts+(Tu-Tsle* 25 A. Draw a graph showing how you expect the object's temperature to change as time passes. come -kt B. Use a graphing calculator or an applet such as https://www.desmos.com/calculator to obtain a graph of T = 55e-kt + 25. Explore the effect of choosing different values for k. (I am using capital-T to represent temperature and small-t to represent time.) The similarity between these graphs and the graph you drew in part A should convince you that T = 55e-kt + 25 is a pretty good guess for how the temperature varies with time. Choose a hist kresulte getting close to 10 Newton proposed that the difference in temperature between the object and its environment decreases at a rate that is proportional to that difference. C. Write an expression for the difference between the environment temperature and the current temperature: Ts- en D. Take the derivative of your expression from C. E. Do your answers to C and D provide agree with Newton's proposal? Explain.
II: Exponential Decay: Newton's Law of Cooling An object at 80° C is in an environment where the temperature is a constant 25° C. (The environment is large enough that the cooling object does not raise the temperature of its surroundings. T₁ surrowing Her To Hory of Tlol: Ts+(Tu-Tsle* 25 A. Draw a graph showing how you expect the object's temperature to change as time passes. come -kt B. Use a graphing calculator or an applet such as https://www.desmos.com/calculator to obtain a graph of T = 55e-kt + 25. Explore the effect of choosing different values for k. (I am using capital-T to represent temperature and small-t to represent time.) The similarity between these graphs and the graph you drew in part A should convince you that T = 55e-kt + 25 is a pretty good guess for how the temperature varies with time. Choose a hist kresulte getting close to 10 Newton proposed that the difference in temperature between the object and its environment decreases at a rate that is proportional to that difference. C. Write an expression for the difference between the environment temperature and the current temperature: Ts- en D. Take the derivative of your expression from C. E. Do your answers to C and D provide agree with Newton's proposal? Explain.
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Transcribed Image Text:STAPLES
II: Exponential Decay: Newton's Law of Cooling
An object at 80° C is in an environment where the temperature is a constant 25° C. (The environment is
large enough that the cooling object does not raise the temperature of its surroundings.
T₁ = surronding topp
To Herry of
TIel: Ts+(To-Tslett
A. Draw a graph showing how you expect the object's temperature to change as time passes.
21
B. Use a graphing calculator or an applet such as https://www.desmos.com/calculator to obtain a graph
of T = 55e-kt + 25. Explore the effect of choosing different values for k. (I am using capital-T to
represent temperature and small-t to represent time.) The similarity between these graphs and the
graph you drew in part A should convince you that T = 55e-kt + 25 is a pretty good guess for how the
temperature varies with time.
Choose adhiste
k result, the
getting close to you
come
Newton proposed that the difference in temperature between the object and its environment
decreases at a rate that is proportional to that difference.
C. Write an expression for the difference between the environment temperature and the current
temperature:
Ts- en
D. Take the derivative of your expression from C.
E. Do your answers to C and D provide agree with Newton's proposal? Explain.
V
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