Answer
See proof
Work Step by Step
The only constant is the constant of proportionality. This is because the rate of change is based upon the constant of proportionality and the difference between the temperature of the two objects in question. No other values are needed. \[ \frac{dT}{dt} = k(T - T_e),\quad T(0) = T_0 \] where: - \(\frac{dT}{dt}\) is the rate of change of temperature, - \(k\) is the constant of proportionality, - \(T\) is the temperature, - \(T_e\) is the temperature of the two objects in question, and - \(T(0)\) is the initial temperature at time \(t = 0\).
