Boris recorded the number of daylight hours on the first day of each month in a northern hemisphere town. This data was plotted onto a scatter diagram. The points were then joined by a smooth curve, with minimum point (0, 8) and maximum point (6, 16) as shown in the following diagram. hours of daylight each day 16 12 6 9 12 month of the year Let the curve in the diagram be y = f(t), where t is the time, measured in months, since Boris first recorded these values. Boris thinks that f(t) might be modelled by a quadratic function. leng (a) Write down one reason why a quadratic function would not be a good model for the number of hours of daylight per day, across a number of years. Paula thinks that a better model is f(t) = a cos(bt) + d, t > 0, for specific values of a, b and d. For Paula's model, use the diagram to write down (b) the amplitude. (c) the period. (d) the equation of the principal axis. (e) Hence or otherwise find the equation of this model in the form: (f) f(t) = a cos(bt) +d For the first year of the model, find the length of time when there 10 hours and 30 minutes of daylight per day. [1]