Suppose that the length of time between consecutive high tid

Suppose that the length of time between consecutive high tides is approximately 12.5 hours. According to the National Oceanic and Atmospheric Administration, on a particular day in a city in Georgia, high tide occurred at

3 : 36

AM

(3.6000

hours) and low tide occurred at

9 : 51

AM

(9.8500

hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was

8.6

feet and the height of the water at low tide was -0.4 foot.


(a) Approximately when will the next high tide be?
___:____ PM (Round to nearest min)


y = A cos (w(x-p)) + B

(b) what is the amplitude? A

(c) w? (type an exact answer with pi)

(d) p? (type four places after the decimal)

(e) B?

(f) now use the function found in part b to predict the height of the water at the next high tide.

y = ?

Solution

a) 3:36+12:30=16:06

b) A = (8.6+.4)/2 = 9/2

c) w=2pi/25, period = 25

d) p = 3.6

e) B= 8.6-4.5= 4.1

f) y = (9/2)cos(2pi/25(x-3.6))+4.1