Question

In Pensacola in June, high tide was at noon. The water level at high tide was 12 feet and 2 feet 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 June for Pensacola as a function of time (t).

Answer 1

@sidsiddhartha @mathmale

Answer 2

high tide is 12 feet, low tide is 2 feet
the middle is \(\frac{12-2}{2}=10\) feet
that makes your amplitude \(5\)
up 5, down 5

Answer 3

half way between 2 and 12 is \(\frac{2+12}{2}=7\) so you are going to have to put a \(+7\) out at the end of your equation

Answer 4

@satellite73 alright!
so it's
f(t) = 5 cos pi/6 t + 7

Answer 5

the fact that the period is \(12\) means for
\[5\cos(bx)+7\] the period is \(12\)
period is always \(\frac{2\pi}{b}\) solve
\[\frac{2\pi}{b}=12\] and solve for \(b\)

Answer 6

yeah, that looks good
assuming we make noon as 0 and time continuing on from there