5 The fuel consumption of a car, \(C\) miles per gallon, varies with the speed, \(v\) miles per hour. Jamal models the fuel consumption of his car by the formula
\(C = \frac { 12 } { 5 } v - \frac { 3 } { 125 } v ^ { 2 }\), for \(0 \leqslant v \leqslant 80\).
- Suggest a reason why Jamal has included an upper limit in his model.
- Determine the speed that gives the maximum fuel consumption.
Amaya's car does more miles per gallon than Jamal's car. She proposes to model the fuel consumption of her car using a formula of the form
\(C = \frac { 12 } { 5 } v - \frac { 3 } { 125 } v ^ { 2 } + k\), for \(0 \leqslant v \leqslant 80\), where \(k\) is a positive constant. - Give a reason why this model is not suitable.
- Suggest a different change to Jamal's formula which would give a more suitable model.