Differential Equation For A Cooling Object

Question

The temperature, $$T(t)$$, of a cooling object in degrees Celsius is a differentiable function of time $$t$$ in minutes. The temperature changes according to the differential equation $$ \frac{dT}{dt} = -kT $$, where $$k$$ is a positive constant. At time $$t=0$$, the temperature is 180°C and is decreasing at a rate of 45°C per minute. Which of the following is an expression for $$T(t)$$?

Accepted Answer

$$ 180e^{-t/4} $$

Answer

$$ -45t + 180 $$

Answer

$$ 180e^{-45t} $$

Answer

$$ e^{-t/4} + 179 $$

Differential Equation For A Cooling Object

Question Leaderboard