SOLUTION: if low tide is 6 ft at 11 pm aturday night and high tide is 14 ft at 5 am sunday morning, write a function of the form h(t)=a sin b(t-h) + k that models the height of the tide t ho

Question 1112227: if low tide is 6 ft at 11 pm aturday night and high tide is 14 ft at 5 am sunday morning, write a function of the form h(t)=a sin b(t-h) + k that models the height of the tide t hours after midnight (12 am sunday).
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
A function is requested to represent water level height in feet,
as a function of in hours after 12 AM Sunday,
hour after low tide at 11 PM Saturday,
and hours before high tide at 5 AM Sunday.
The function must be of the form
.
The water level, , ranges from ft to ft.
That means that the sinusoidal water level function
has an amplitude (in feet) such that
is the range around an average level (in feet) .
So, and .
The time from low tide to high tide (in hours) is ,
so the period of the function (in hours) is
(from low tide to next low tide).
That makes , and ,
so that when (and change by ,
changes by .
After low tide, the water level will reach its average height
hours later at 2AM on Sunday, which is ,
and keep increasing.
So ,
,
.
If is increasing at ,
that means or a multiple of .
From , we get as the simplest option.
Of course, for any integer would also
make , with increasing at .
In sum, .

CHECKING:
At 11 PM Saturday, and
.
At 5 AM Sunday, and
.
The graph of is

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