Respuesta :
Question:
Write a cosine function of the form f(t)= Acos(Bt) where A and B are real numbers that models the water level f(t) as a function of time measured in t hours since 8:30 a.m.
Answer:
The equation of the cosine function that models the water level as a function of time is;
[tex]f(t) = -4\times cos(\frac{2\pi }{13} t)[/tex]
Step-by-step explanation:
From the required equation, we have for a wave form
f(t) = A·cos(B·t)
A = Amplitude of the wave
B = The period of the wave
t = Time of wave
The period can be derived as follows
We have 7:30 to 1:00 is 5.5 hrs, therefore one full cycle occurs in 11 hours
The period is given by;
[tex]Period = \frac{2\pi }{B}[/tex]
Therefore,
[tex]\frac{2\pi }{B} = \frac{13}{1}[/tex] so that
[tex]The \, period \, B = \frac{2\pi }{13}[/tex]
The amplitude is given as the maximum displacement from the position at rest. Therefore, the amplitude = (15 - 7)/2 = 4 feet
Therefore the equation of the cosine function that models the water level as a function of time is;
[tex]f(t) = -4\times cos(\frac{2\pi }{13} t)[/tex].
