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The Ancient Murrelet is a plucky little bird of the auk family that lives in colonies on islands off the northern Pacific 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 floor, 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 function that describes the observable decline: P(t) = 5-√√2t+4 where P(t) is the island population in thousands and t 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 P-intercept of this function. Clearly show your method. d) Find the coordinates of the f-intercept of this function. Clearly show your method.

The Ancient Murrelet is a plucky little bird of the auk family that lives in colonies on islands off the northern Pacific 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 floor, 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 function that describes the observable decline: P(t) = 5-√√2t+4 where P(t) is the island population in thousands and t 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 P-intercept of this function. Clearly show your method. d) Find the coordinates of the f-intercept of this function. Clearly show your method.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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The Ancient Murrelet is a plucky little bird of the auk family that lives in colonies on islands off the northern Pacific 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 floor, 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 function that describes the observable decline: P(t) = 5-√√2t+4 where P(t) is the island population in thousands and t 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 P-intercept of this function. Clearly show your method. d) Find the coordinates of the t-intercept of this function. Clearly show your method.
Transcribed Image Text:The Ancient Murrelet is a plucky little bird of the auk family that lives in colonies on islands off the northern Pacific 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 floor, 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 function that describes the observable decline: P(t) = 5-√√2t+4 where P(t) is the island population in thousands and t 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 P-intercept of this function. Clearly show your method. d) Find the coordinates of the t-intercept of this function. Clearly show your method.
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e) Using the coordinates from parts b) - d), graph the function on its mathematical domain. Check your graph with DESMOS. Properly label the graph. f) Interpret, in one sentence, the meaning of each intercept in the problem context. g) Given the problem context, what is the practical domain? Express this interval notation: h) 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? Show the algebra: i) 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: Right side end-behaviour: j) Find on the interval t € [0,2.5]. Show your work and show the secant line for this interval on your DESMOS graph above.
Transcribed Image Text:e) Using the coordinates from parts b) - d), graph the function on its mathematical domain. Check your graph with DESMOS. Properly label the graph. f) Interpret, in one sentence, the meaning of each intercept in the problem context. g) Given the problem context, what is the practical domain? Express this interval notation: h) 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? Show the algebra: i) 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: Right side end-behaviour: j) Find on the interval t € [0,2.5]. Show your work and show the secant line for this interval on your DESMOS graph above.
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