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AP Calculus AB/Unit 7: Differential Equations
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Newton's Law of Cooling Model

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The temperature, TT, of an object cooling in a room with a constant temperature of 20 °C20\,°C is described by the differential equation dTdt=−k(T−20)\frac{dT}{dt}=-k(T-20), where kk is a positive constant. If the object’s temperature is initially 80 °C80\,°C, which of the following is the solution for T(t)T(t)?

A

T(t)=20−60∗e−k∗tT(t)= 20-60*e^{-k*t}

B

T(t)=20+60∗e−k∗tT(t)= 20+60*e^{-k*t}

C

T(t)=80∗e−k∗tT(t)= 80*e^{-k*t}

D

T(t)=20+60∗ek∗tT(t)= 20+60*e^{k*t}

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