Question
On a typical day at an ocean port, the water has a maximum depth of 18m at 6:00 am. The minimum depth of 9m occurs 6.8 hours later. Write an equation to describe the relationship between the depth and time.
Answers
the period is 2*6.8 = 13.6, so we have
d(t) = a*cos(2pi/13.6 t) = a*cos(.462t)
The max-min range is 18-9 = 9, so the amplitude is 4.5 and we have
d(t) = 4.5 cos(.462t)
If we call t is the hour of the day, then max is at t=6, so
d(t) = 4.5 cos(.462(t-6))
Since the average depth is (9+18)/2, we have
d(t) = 4.5 cos(.462(t-6)) + 13.5
To see the graph, visit
http://rechneronline.de/function-graphs/
enter the function as
4.5 cos(.462*(x-6))+13.5
and set the x-range at 0-20
the y-range at 0-20
d(t) = a*cos(2pi/13.6 t) = a*cos(.462t)
The max-min range is 18-9 = 9, so the amplitude is 4.5 and we have
d(t) = 4.5 cos(.462t)
If we call t is the hour of the day, then max is at t=6, so
d(t) = 4.5 cos(.462(t-6))
Since the average depth is (9+18)/2, we have
d(t) = 4.5 cos(.462(t-6)) + 13.5
To see the graph, visit
http://rechneronline.de/function-graphs/
enter the function as
4.5 cos(.462*(x-6))+13.5
and set the x-range at 0-20
the y-range at 0-20