It is estimated that nearly 80% of the world's population of Sandhill Cranes migrate through central Nebraska twice each year. Suppose that we may model the crane population along the Platte River, in thousands of cranes, using the following function: $$P(t) = 300\cos\big(\frac{\pi}{6}t-\pi\big) + 300$$ where $t$ is in months after January 1, 2016.

(a) Which of the following is the graph of $P(t)$ on the interval $[0,18]$? Select A B C D None of the graphs below

(b) Assuming the model holds, find all times $t$ when there are approximately 360 thousand cranes along the Platte River.

where $n$ is any integer, and both values of $t$ are between $0$ and $12$.

Use radian measure and enter your answers using at least four significant digits.

(c) Based on the graph above, how many times will the Sandhill Crane population be equal to 360 thousand on the interval $[0,18]$? times

(d) Use your solutions to parts (a) through (c) to find all times $t$ in the interval $[0,18]$ such that there are approximately 360 thousand cranes. Enter your answer as a comma separated list. Use radian measure and round your answer to at least four significant digits. .

Hint: