Question

N Panama City in January, high tide was at midnight. The water level at high tide was 9 feet and 1 foot 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 January for Panama City as a function of time (t).

f(t) = 4 cospi over 2t + 5 f(t) = 5 cospi over 2t + 4 f(t) = 5 cospi over 6t + 4 f(t) = 4 cospi over 6t + 5

Answer 1

f(t) = 4 cos pi over 6t + 5

Explanation:

First find the amplitude \

9-1=8/2=4

Then the midline

9+1=10/2=5

Then we solve fore b

2pi/b=12/1➡2pi=12b➡b=2pi/12=pi/6

Then we put it together the amplitude being a the midline is d and we just did b so the correct option would be

f(t) = 4 cos pi over 6t + 5

Answer 2

The period of this function ( cos (bx) ):
T =
`(2 \pi )/(b)=12`
b=
`(2 \pi )/(12) = ( \pi )/(6)`
Maximum tide : 9 feet (for cos value 1) f(t)=4*1 + 5 = 9
Minimum tide: 1 feet ( for cos value -1) f(t) = 4*(-1) + 5 =1
Answer: D) f(t)= 4 cos (π/6 t) +5