CPhill

I think the function might be

y =15 cos [ (2pi/365) t ] + 43

The water level is at a max at day 0  =  58 cm

The water level is at 30 cm about 153 days after this

I used x for t   here :

Thanks, HMB.....!!!!

You are close...HMB....!!!

The equation of the midline is  y = - 3

3.  The equation is

y = 2cos (2x) - 3

All we can do is to solve for x

y = 4 + 2x

 y - 4 = 2x

[ y - 4 ] / 2   =  x

A.  The radius can be found as 

[ highest point - lowest point ] / 2  = [55 - 5 ] / 2   =  50 / 2   =   25  yd

So A is true

B.  False....the lowest point is at 9 seconds

C. False....max height = 55 yd

D True

We have the form

f(x) = A sin (Bx) +  D

A = the amplitude =  [ highest point - lowest point] / 2 =  [ 10.2 - .1] / 2 = 10.1/2 = 5.05

The period is 24

B = 2pi / period =  2pi /24  =  pi/12

D = the midline =  (highest point + lowest point] ) / 2  =  (10.2 + 0.1) / 2 = 10.3 /2 = 5.15

So....the equation is

f(x) = 5.05sin [ (pi/12) x ] + 5.15

The graph is horizontally compressed by a factor of 2 and shifted up 1 unit

OK....I'll post a pic

Note....one min point occurs at  -pi/4

The next min occurs at   (pi + pi/2) /2  =    (3pi /2) * (1/2)  = 3pi/4

So.....the period is

(3pi/4   -   - pi/4)  =   4pi/4  =   pi

We have the form

y = Asin (Bx) 

The amplitude, A, is  [ difference between highest and lowest points ] / 2  = 10/2 =  5

The period is 12 sec

B  =   2pi / period   =  2pi/ 12  =  pi/6

So.....the equation of the function is

y = 5sin [ ( pi / 6) x  ]

Here's the graph : https://www.desmos.com/calculator/6ejfoskflu