a

Suppose the population of a coastal city follows a sinusoidal pattern due to seasonal migration. The population of the city over the course of a year can be modeled by the equation: $P(t) = 70000 + 10000\cos\left(\dfrac{\pi}{6}t - \dfrac{\pi}{2}\right)$, $P(t)$ is the population at time $t$ ($t$ is the time in months, with $t = 0$ corresponding to January 1st).