Calculus
posted by Jillian .
What would the values of A, B, and C be in this problem?
The tides in a particular bay can be modeled with an equation of the form d= A cos (Bt) + C, where t represents the number of hours since hightide and d represents the depth of water in the bay. The maximum depth of water is 36 feet, the minimum depth is 22 feet and hightide is hitting every 12 hours.

max  min = 3622 = 14
so the amplitude is 7
what do we have to add to 7 to get 36 ?  29
period of cosine curve = 2π/k
12 = 2π/k
k = π/6
so d = 7 cos (πt/6) + 29
check:
at t=0 , d = 7cos 0 + 29 = 36 > high tide
at t=3 , d = 7cos π/2 + 29 = 29 > makes sense
at t=6 , d = 7cos π + 29 = 7+29 = 22 > low tide
at t=9 , d = 7cos 3π/2 + 29 = 29 >makes sense
at t=12, d = 7cos 2π + 29 = 7(1)+29 = 36 > back to high tide 
What will the graph look like for two full periods?

first period:
mark off from 0 to 12, with marks at 0, 3, 6, 9, and 12
at 0 , d=36
at 3, d= 29
at 6, d = 22
at 9, d = 29
at 12, d = 36  end of first period, now repeat that
draw a smoth cosine curve .
(I am somewhat surprised you even asked that question)
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