APFIVE Exponential Decay Initial Value Problem
The temperature of a cooling object is given by a differentiable function $$ T $$, where $$ T(t) $$ is measured in degrees Celsius and $$ t $$ is measured in minutes. The temperature decreases according to the equation
$$ \frac{dT}{dt} = -kT, $$
where $$ k $$ is a positive constant. At time $$ t = 0 $$, the temperature is 180°C and is decreasing at the rate of 45°C per minute. Which of the following is an expression for $$ T(t) $$?
A
$$ 180e^{-45t} $$
B
$$ e^{-t/4} + 179 $$
C
$$ 180e^{-t/4} $$
D
$$ -45t + 180 $$
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