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

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Differential Equations

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Question

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

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