Answer:
![y(t) = 6 -3cos(\frac{2\pi }{14} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-3cos%28%5Cfrac%7B2%5Cpi%20%7D%7B14%7D%20%29t)
![y(t) = 6 -3cos(\frac{2\pi }{7} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-3cos%28%5Cfrac%7B2%5Cpi%20%7D%7B7%7D%20%29t)
![y(t) = 6 - 6cos(\frac{2\pi }{14} ) t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-%206cos%28%5Cfrac%7B2%5Cpi%20%7D%7B14%7D%20%29%20t)
![y(t) = 3- 6cos(\frac{2\pi }{7} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%203-%206cos%28%5Cfrac%7B2%5Cpi%20%7D%7B7%7D%20%29t)
Step-by-step explanation:
Given that,
Hudson Bay tides vary between
and
.
Tide is at its lowest when ![t=0](https://tex.z-dn.net/?f=t%3D0)
Completes a full cycle in 14 hours.
To find:- What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
So, The periodic function of this model is
...................(1)
where, ![A- Amplitude of cycle](https://tex.z-dn.net/?f=A-%20Amplitude%20of%20cycle)
![\omega = Angular speed (in Radian.)](https://tex.z-dn.net/?f=%5Comega%20%3D%20Angular%20speed%20%28in%20Radian.%29)
Then putting the value in given Equation(1) we get,
Amplitude = ![\frac{9-3}{2} ft = 3ft](https://tex.z-dn.net/?f=%5Cfrac%7B9-3%7D%7B2%7D%20ft%20%3D%203ft)
![y^{'} = (3+ 3 )ft = 6ft](https://tex.z-dn.net/?f=y%5E%7B%27%7D%20%3D%20%283%2B%203%20%29ft%20%3D%206ft)
Now, At
it complete full cycle in
because it is at lowest at t=0sec.
∵ ![\omega t= 2\pi](https://tex.z-dn.net/?f=%5Comega%20t%3D%202%5Cpi)
![\omega (t+14) = 2\pi](https://tex.z-dn.net/?f=%5Comega%20%28t%2B14%29%20%3D%202%5Cpi)
∴
Hence ![y(t) = 6 -3cos(\frac{2\pi }{14} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-3cos%28%5Cfrac%7B2%5Cpi%20%7D%7B14%7D%20%29t)
![y(t) = 6 -3cos(\frac{2\pi }{7} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-3cos%28%5Cfrac%7B2%5Cpi%20%7D%7B7%7D%20%29t)
![y(t) = 6 - 6cos(\frac{2\pi }{14} ) t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-%206cos%28%5Cfrac%7B2%5Cpi%20%7D%7B14%7D%20%29%20t)
![y(t) = 3- 6cos(\frac{2\pi }{7} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%203-%206cos%28%5Cfrac%7B2%5Cpi%20%7D%7B7%7D%20%29t)