Young Tovy lives next to the ocean. He likes to wade to a small island very close to shore, but can wade to the island only when the depth of the water is 1.2 metres or less. The depth of the water is determined by the tide. Tovy and a few of his friends want to go to the island for a picnic on Tuesday, and so they need to know when it is safe to wade across to the island. They measure the water depths on Monday (the day before the picnic), and the results are as follows:

Time

5:30

7:15

8:15

10:45

12:00

18:30

19:30

Depth(m)

2.10

0.73

0.43

1.62

2.77

1.49

0.77

The time is in hours and minutes, and so 5:30 is the same as 5.5 hours.

**A.**Write a sinusoidal equation that represents the data. Round the parameters to two decimal places.

**B.**Draw a graph using IT that shows the water depths for two days (Monday and Tuesday).

**C**. Calculate the depth of the water at noon on Tuesday. Show how you arrive at your answer.

**D.**What are the maximum and minimum water depths?

**E.**They want to go on the picnic as close to the middle of the day (on Tuesday) as possible. When can they go to the island, and by when do they have to return? Explain how you arrive at your answer.