Problem

Question 3 of 6 Submit Test 22-23 Precalculus Final Part 1 Question 1-3 In Tau Lake, the water level rises and falls over a consistent period of time. The water typically attains its highot level at "high tide" occurs at $5 \mathrm{am}$, the water level is $8 "$ above sea level. Six hours later, at low tide, the water level is 2" above sea level. Which of the fo level as a function of time after midnight? $f(x)=3 \sin \left(\frac{\pi}{6}(x-2)\right)+5$ $f(x)=3 \cos \left(\frac{\pi}{6}(x-2)\right)+5$ $f(x)=5 \sin \left(\frac{\pi}{6}(x-2)\right)+3$ $f(x)=5 \cos \left(\frac{\pi}{6}(x-2)\right)+3$ Previounfiry fittp Gia. performancematters. com/ola/ola.jsp? clientCode=mdBaltimorecsd\&testld $=30058578 t e s t E v e n t l d=3007723 \& 1 t i L a u n c h \#$

Solution

Step 1 :Test each function at x = 5 and x = 11

Step 2 :Only the first function gives the correct water levels at 5 am (8") and 11 am (2")

Step 3 :\( \boxed{f(x)=3 \sin \left(\frac{\pi}{6}(x-2)\right)+5} \)

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