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 = 1000, k = 9, c = 0.2, and 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 ast→ o? P(t) = Does the graph shown confirm your calculations? P 1000 800 600 400 200 10 30 40 Yes No 20 O O

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 = 1000, k = 9, c = 0.2, and 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 ast→ o? P(t) = Does the graph shown confirm your calculations? P 1000 800 600 400 200 10 30 40 Yes No 20 O O

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

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