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If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equals 0.4. Suppose the ambient temperature TA(t) is equal to a constant 84 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object.

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Answer:

[tex]\dfrac{dT}{dt}=-0.4(T_o-84)[/tex]

Explanation:

dT = Change in temperature

dt = Time interval

k = constant of proportionality = 0.4

[tex]T_o[/tex] = Temperature of object

[tex]T_A[/tex] = Temperature of ambiance = 84°C

From Newton's law of cooling we have the expression

[tex]\dfrac{dT}{dt}=-k(T_o-T_A)[/tex]

So, the differential equation is

[tex]\mathbf{\dfrac{dT}{dt}=-0.4(T_o-84)}[/tex]

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