2. The number of ants in an ant colony changes over time and follows a sinusoidal pattern. After observing It for some time, It's noted that the colony reaches a maximum population of 688 ants after 8 days, and minimum of 516 ants after 19 days. a) Use the data to determine a trigonometric model for the population, P(t), after t days. [4 marks] P(t) = b) Use your model to algebraically approximate the number of ants where will be in the colony after 180 days. [2 marks] C) Include your graph from Desmos. It should show the data points and your model. [4 marks] Marks will be deducted if you do not use reasonable x and y scales to represent the situation