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Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: P(t) = 1+ ke-ct

Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: P(t) = 1+ ke-ct

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: d. P(t) 1 + ke-ct where c, d, and k are positive constants. For a certain fish population in a small pond d = 1200, k = 11, c = 0.2, and t is measured in years. The fish were introduced into the pond at time t = 0. (a) How many fish were originally put in the pond? fish (b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.) 10 years fish 20 years fish 30 years fish (c) Evaluate P(t) for large values of t. What value does the population approach as t → o? P(t) = Does the graph shown confirm your calculations? 1200 1000 800 600 400 200 10 20 30 40 Yes O No O O
Transcribed Image Text:Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: d. P(t) 1 + ke-ct where c, d, and k are positive constants. For a certain fish population in a small pond d = 1200, k = 11, c = 0.2, and t is measured in years. The fish were introduced into the pond at time t = 0. (a) How many fish were originally put in the pond? fish (b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.) 10 years fish 20 years fish 30 years fish (c) Evaluate P(t) for large values of t. What value does the population approach as t → o? P(t) = Does the graph shown confirm your calculations? 1200 1000 800 600 400 200 10 20 30 40 Yes O No O O
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