Question

The times of sunrise in Auckland can be modelled by the function
where t is the time in minutes after midnight
and d is the number of days after 1 January 2009.

Use the model to answer these questions.

(a) How many minutes are there between the earliest sunrise and the latest sunrise?

(b) How many days are there between the date of the earliest sunrise and the date of the latest sunrise?

(c) What is the time of sunrise 25 days after the 1st January?

(d) What is the second day in the year that has a sunrise at 7:05 am?