Suppose that the length of time between consecutive high tides is approximately 12.5 hours, IE this 12.5 hours is our period because it's from 1 high tide to the next high tide. According to the National Oceanic and Atmospheric Administration, on a particular day in a city in Georgia, high tide occurred at 3:34 AM or 3.5667 hours, and low tide occurred at 9.8167 hours. Water heights are measured as the amount above or below the mean lower low water. Above or below the mean lower low water. The height of the water is 8.2 feet above, so we're going to have 8.2 feet above and then we're going to have negative .8 feet below. So when we want to figure out the amplitude, oh, when we want to figure out the amplitude, we're going to take this whole distance and then divide by two. So 8.2 -, -.8 / 2. So that's going to be 9 / 2 or 4.5. So that's where this amplitude came from. It says approximately when will the next high tide occur. Well, if we know that the period's 12.5, if we thought about 334 + 12 hours and .5 is really 30 minutes, we can see that that's really going to be 16 O 4. But if we subtract 12, that would be 4 O 4:00 PM. So the next thing we want to do is we want to figure out what the Omega is. So we know that the regular period of sinus 2π, so 2π divided by Omega, we frequently use B. They're just variables. But 2π over Omega is going to equal 12.5. Well if I think about 12.5, that's 12 1/2 so that's really 25 halves. Remember we take this two in the denominator, multiply it by the whole quantity. So 2 * 12 is 24 plus the one in the numerator, so 25 halves. Then if we cross multiply we can see we get 4 Pi equaling 25 Omega. And to get a mega by itself, we just divide by 25. So Omega is four π / 25, which is what we got right there. The fee we have to think about and the fee is going to be the 12.5 / 4. So actually let's use this 25 halves divided by 4 increments, so 25 halves times 1/4. So that gives me 25 eighths and 25 eighths is 3.125. And then we're going to have the shift from the 3.5667. So if I have 3.5667 -3.125, I don't, let's see, 24. Oh, I'm off by a decimal place. So hold on a SEC 3.567.4417 and then we need to take that .4417 and multiply it by four π / 25 S If I grab my calculator .4417 * 4π / 25 S .2220226. So when I come back in here, that's where this .2220 came from. Finally, our B is just going to be the sum of the two extremes. So 8.2 + -.8 all over 2. So that would be 7.4 / 2 which would be the 3.7 there. So the next part says draw the graph. So using all this given information, if we want to draw the graph, we can see that our amplitude was going to be whatever it was something. Now let's go back. Our amplitude is going to be 4.5, but we're going to go from a high of 8.2 to a negative .8. So when I look at these four choices, I know I need to have a negative. So A or C would be my only choices to start. And then it tells me that high tide occurs at 3:34. Well, if I look here at 334, that's not high tide. So that has to be letter C. That's going to give us what we need. We needed a negative .8. We needed a high of 8.2. We needed to have the height occurring at 3:34 AM. So then it says use the function found in Part B to predict the height. So we're going to take all that information and we're going to input it into the calculator. So we're going to have calculator 4.5 times the sine of four π / 25 times 16.0667. That's the next time we're going to have high tide minus .222. close my parentheses plus 3.7. So if you don't remember, looking back at the problem, we needed to figure out the next high tide, which was going to be this 16.0667. If I take 3.5667 and I'm or and I add 12.5 to it, that's my 16.0667. So going back to our calculator, if we hit enter we get 8.1999985 and the directions tell us to Round 2 decimal places. I think 01 decimal place, so 8.2.