Determine average rate of change in a variety of practical contexts.

A water tank initially contains 12,000 litres. After 8 hours of operation, the tank holds 3,200 litres. What is the average rate of change of the water volume, in litres per hour?

A mobile phone battery's charge level is modelled by the function $C(t) = 100 - 8t + 0.5t^2$, where $C(t)$ is the percentage charge remaining and $t$ is the time elapsed in hours since the phone was left unplugged. Determine the average rate of change of the battery charge between $t = 2$ hours and $t = 5$ hours. Express your answer in percentage per hour.

A pharmaceutical company is developing a controlled-release medication. The concentration of the drug in the bloodstream is modelled by \( C(t) = 15te^{-0.3t} \), where \( C(t) \) is measured in micrograms per millilitre (μg/mL) and \( t \) is the time in hours after administration, for \( 0 \leq t \leq 12 \). Determine the average rate of change of drug concentration between \( t = 2 \) hours and \( t = 8 \) hours. Express your answer correct to two decimal places.

A manufacturing plant monitors the temperature, \(T\) degrees Celsius, of a chemical reactor over a 10-hour production cycle. The temperature data recorded at various times are shown in the table below. Determine the average rate of change of temperature during the interval from \(t = 2\) hours to \(t = 8\) hours, giving your answer in degrees Celsius per hour correct to two decimal places.

A cylindrical water tank is being filled and drained simultaneously during a 10-hour period. The volume of water in the tank at time \(t\) hours is modelled by \(V(t) = 850 + 120\sin\left(\frac{\pi t}{5}\right) - 15t\), where \(V(t)\) is measured in litres and \(0 \le t \le 10\). Determine the average rate of change of the volume of water in the tank over the 10-hour period, giving your answer correct to two decimal places.