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-ctwhere 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 yearsfish20 yearsfish30 yearsfish(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?1200100080060040020010203040YesO NoO O

Answered: Animal populations are not capable of…

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)

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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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 = 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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