Answer
$d= -6.5 \cos (\dfrac{\pi}{6})t+10$
Work Step by Step
From the table we have $M=16.5 ; m=3.5$
Amplitude, $|a|= \dfrac{M-m}{2}= \dfrac{16.5-3.5}{2}=6.5$
Vertical amplitude, $k= \dfrac{M+m}{2}= \dfrac{16.5+3.5}{2}=10$
Here, the period is: $P=2(6) =12 hours$
and $p=\dfrac{2 \pi}{B}=12 \implies B=\dfrac{\pi}{6}$
We can see that the graph is minimum at $t=0$; this means that we will use the cosine model that is reflected in the x-axis with no horizontal shift, that is, $h=0$
Hence, the model is: $d= -6.5 \cos (\dfrac{\pi}{6})t+10$
