Water levels during global warming

Question

Water levels near a glacier currently average 9 feet, varying seasonally by 2 inches above and below the average and reaching their highest point in January. Due to global warming, the glacier has begun melting faster than normal. Every year, the water levels rise by a steady 3 inches. Find a function modeling the depth of the water t months from now. I don't know how they come up with this model: D(t) = 2cos(π/6 * t) +108 + 1/4*t

Answer 1

In inches, the average level is $108$. We need to add a period-$12$ mean-$0$ term to this to get what would happen without global warming. This gives $108+A\cos\frac{\pi t}{6}$ for some $A$, provided we choose $t=0$ to denote a seasonal peak. The amplitude $A$ has to be $2$, so the seasonal variation is $2$ inches above or below the average. Finally, each month sees a quarter-inch trendline rise from global warming, giving the stated $D(t)$.