## Precalculus (6th Edition) Blitzer

Based on the given data, we can make a graph as shown in the figure. It can be seen that the pattern resembles a sine curve $y=38+15sin(\omega t+\phi)$. As the period is $p=12$ hours, we have $\omega=\frac{2\pi}{p}=\frac{\pi}{6}$. At $t=0, y=23$, we have $sin\phi=-1$ and $\phi=-\frac{\pi}{2}$; thus $y=38+15sin(\frac{\pi}{6} t-\frac{\pi}{2})$.