1. A gardener is modelling the number of hours of daylight his allotment receives at different times of the year using the function

$h(t)=12+5sin(\frac{2 \pi t}{365})t\geq0$

where $h$ is the number of hours of daylight on a given day, and $t$ is the time measured in whole days.  Note that $t=0$ corresponds to the first day of the model.

(i) Find the number of hours of daylight on the 100^th day.

(ii)Write down the maximum and minimum number of daylight hours the model predicts.

(iii) Assuming the allotment is located in the UK, give a reason why the first day of the model most likely does not correspond to 1^st january.