A cup of coffee, cooling off in a room at temperature $21^\circ \text{C}$, has cooling constant $k = 0.118 \, \text{min}^{-1}$.

(a) How fast is the coffee cooling (in degrees per minute) when its temperature is $T = 76^\circ \text{C}$?

Cooling at the rate = $\frac{{}^\circ \text{C}} {\text{min}}$

(b) Use the Linear Approximation to estimate the change in temperature over the next $6\, \text{s}$ when $T = 76^\circ \text{C}$.

Estimated to cool = ${}^\circ \text{C}$ over the next $6\, \text{s}$

(c) The coffee is served at a temperature of $88^\circ \text{C}$. How long should you wait before drinking it if the optimal temperature is $61^\circ \text{C}$?

Waiting time = $\text{min}$