newton's law of cooling

]> newton's law of cooling

\frac{d T}{d t} = k [T - T_{m}]

\frac{d T}{[T - T_{m}]} = k d t

\int \frac{d T}{[T - T_{m}]} = k \int d t

\ln | T - T_{m} | = k t + c_{2}

e^{\ln | T - T_{m} |} = e^{k t + c}

| T - T_{m} | = e^{k t} e^{c}

T - T_{m} = c e^{k t}