Question

In Pensacola in June, high tide was at noon. The water level at high tide was 12 feet and 2 feet at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in June for Pensacola as a function of time (t).

f(t) = 12 cospi over 2t + 5

f(t) = 5 cospi over 2t + 12

f(t) = 5 cospi over 6t + 7

f(t) = 7 cospi over 6t + 12

Answer 1

Hey there @mathhelpnow ,
This is a way you can tackle this problem. High tide at noon is 12 feet, meaning f(0)=12; and next high tide is exactly 12 hours later ie. f(12)=12. You'd also want a low tide between each 2 high tides ie. f(6)=2
The only option in your choices that verifies this is: \[f(x)=5\cos(\frac{ \pi }{ 6 }t)+7\] a.k.a. option 3.

Answer 2

Thanks for explaining!:)

Answer 3

No problem, have a good day !