STATEMENT OF THE PROBLEM

Coast Guard instruments were used to take hourly readings of the height of the water in Oakland Bay on a given day. The findings are recorded in the table below.

TIME WATER LEVEL (in feet)

Midnight 15.63
1 a.m. 18.04
2 a.m. 19.53
3 a.m. 20.35
4 a.m. 19.74
5 a.m. 17.82
6 a.m. 15.63
7 a.m. 12.54
8 a.m. 11.19
9 a.m. 10.20
10 a.m. 10.96
11 a.m. 13.14
Noon 15.17
1. p.m. 18.04
2 p.m. 19.49
3 p.m 20.00
4 p.m. 19.87
5 p.m 17.77
6 p.m. 15.55
7 p.m 13.15
8 p.m. 10.82
9 p.m 10.38
10 p.m. 10.70
11 p.m 12.89
Midnight 15.21

PART A:
Based on these data points, find a function that "best" models the height of the water at any time t.

PART B:
Approximate what the height of the water was at 1:30 p.m. on that day. Explain your conclusions.

PART C:
Was the water level rising or falling at 1:30 p.m.?

PART D:
Approximate what the height of the water was at 3:30 p.m. on that day.
Explain your conclusions.

PART E:
Approximately how fast was the water level falling at 7 a.m.?

PART F
Approximate all the times within the first 12 hours at which the water level will be 18 feet.