The depth of water in a harbour varies as a function of time. The maximum depth is 9 feet and the minimum depth is 1 foot. The depth can be modelled with a sinusoidal function that has a period of 12 hours. If the depth is 5 feet at 12 midnight, and is increasing,

a. Create an algebraic model to predict the depth of the water as a function of time. Justify your reasoning.

b. The water must be at least 7 feet for Annie's fishing boat to safely navigate the harbour. She wants to enter the harbour during the afternoon.

i. Create a graph of this function using technology.

ii. What is the earliest time she can enter the harbour?

iii. How long can she safely stay in the harbour? [T2]