Tutorial 2 Math 0130 Ancient Murrelet Population Study The Ancient Murrelet is a plucky little bird of the an]: family that lives in colonies on islands oif the northern Pacic coasts of Russia, Alaska and Canada. Half of the world population breeds on the islands of Haida Gwaii, British Columbia. Since these birds lay their eggs in burrows on the forest oor, the nestlings are highly susceptible to predation. Their populations have been greatly reduced over the past century by mammalian predators (deer, raccoons, rats) introduced to their breeding islands after contact was established between the Haida people and outsiders. Conservation efforts have only recently been undertaken. A multi-year population study on one island, now closed to human visitors, has produced the following mction that describes the observable decline: P(t)=5y'2t+4 where P(t) is the island population in thousands andt is the time in years since January 1, 2008, when the study was started. The goal is to graph and interpret this function in this problem context. a) Algebraically find the mathematical domain of this function and express your answer in interval notation. b) Use the domain to find the coordinates of the boundary value of this function. c) Find the coordinates of the Pintercept of this function. Clearly show your method. d) Find the coordinates of the tintorcopt of this function. Clearly show your method. e) Using the coordinates from parts b) - d), graph the function on its mathematical domain. Check your graph with DESMOS. A proper hand-drawn graph is expected on graph paper, using no more than 1f3 of your page. Properly label and title the graph. e) Interpret, in one sentence, the meaning of each intercept in the problem context f) Given the problem context, what is the practical domain? Express this interval notation. g) Biologists agree that a population must have a minimum colony size of 1000 to be self-sustaining. By what year must active conservation efforts be undertaken on this island? h) Analyze this graph on the mathematical domain by stating the following (where applicable), using the appropriate notation: Range Maxima Minima Intervals of Increase Intervals of Decrease Left side end-behaviour Right side end-behaviour