Interpret piece-wise linear graphs and step graphs used to model practical situations.

A water reservoir uses a stepped pricing model where the cost per kilolitre changes based on total consumption. The graph below shows the total cost \(C\) (in dollars) as a function of water consumption \(V\) (in kilolitres) for a quarterly billing period. (a) Interpret the slope of the graph in the interval \(40 < V \le 80\). (1 mark) (b) Interpret the meaning of the point where the graph changes at \(V = 80\). (1 mark) (c) Calculate the cost per kilolitre for consumption between 80 kL and 120 kL. (1 mark) (d) A household uses 95 kL in a quarter. Determine the total amount they pay. (1 mark)

A car rental company charges a daily base fee plus a cost per kilometre driven. The total daily cost \(C\) (in dollars) is modelled by the piece-wise linear function shown in the graph below, where \(d\) represents the distance driven (in km). (a) Interpret the cost when no distance is driven. (1 mark) (b) Interpret the rate of change in cost for the interval \(0 \leq d \leq 100\). (1 mark) (c) Interpret the rate of change in cost for the interval \(d > 100\). (1 mark)

A taxi company uses the fare structure shown in the graph below, where \(C\) is the total fare in dollars and \(d\) is the distance travelled in kilometres. (a) Interpret the \(C\)-intercept of the graph. (1 mark) (b) Interpret the rate of change of the fare for the distance interval from \(0\) km to \(5\) km. (1 mark) (c) Determine the total fare for a journey of \(8\) km. (1 mark)