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. 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 t is measured in years. The fish were introduced che 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 fish 20 years 30 years fish (c) Evaluate P(t) for large values of t. What value does the population approach ast → ∞? P(t) = Does the graph shown confirm your calculations?
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. 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 t is measured in years. The fish were introduced che 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 fish 20 years 30 years fish (c) Evaluate P(t) for large values of t. What value does the population approach ast → ∞? P(t) = Does the graph shown confirm your calculations?
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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