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AP Calculus AB/Unit 7: Differential Equations
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Exponential Decay Initial Value Problem

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The temperature of a cooling object is represented by a differentiable function TT, where T(t)T(t) is the temperature in degrees Celsius at time tt in minutes. The rate of change of the temperature is given by the differential equation dTdt=−kT \frac{dT}{dt} = -kT , where kk is a positive constant. At time t=0t=0, the temperature is 180°C and is decreasing at a rate of 45°C per minute. Which of the following is an expression for T(t)T(t)?

A

180e−45t 180e^{-45t}

B

e−t/4+179 e^{-t/4} + 179

C

−45t+180 -45t + 180

D

180e−t/4 180e^{-t/4}

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