Predators and Prey Natural Resources personnel recorded data on deer and wolf populations in an area of Ontario. Year Number of Adult Deer Number of Adult Wolves 2010 340 550 2011 315 480 2012 305 380 2013 330 300 2014 355 405 2012 305 560 2016 300 500 2017 320 445 2018 345 385 2019 365 455 2020 340 640 2021 310 560 1. With or without the use of technology, plot the two sets of data on the same grid, one set or the prey (deer) and one set for the predators (wolves). 2. In your notebook, sketch a curve of best fit for each data set. 3. Find the equation of the curve of best fit for each data set, using Desmos' regression tool. 4. Discuss the characteristics of each curve: a. Maximum and minimum populations b. Average increase in population from trough to peak 5. What is the phase shift between the two curves? What is the real world explanation for this phase shift? 6. Why are sinusoidal models appropriate for this data? 7. The two curves intersect at various times. Interpret these points of intersection in terms of population. Choose one point of intersection and determine the instantaneous rate of change for each population at that time. Interpret your results. 9. Can you think of another real world situation in which pairs are related in the same way? Justify your answer in writing