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 where c, d, and k are positive constants. For a certain fish population in a small pond d = 1400, k = 13, 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 - co? P(t) = Does the graph shown confirm your calculations? 1400 1200 1000 800 600 400 200 10 20 30 40 O Yes
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 where c, d, and k are positive constants. For a certain fish population in a small pond d = 1400, k = 13, 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 - co? P(t) = Does the graph shown confirm your calculations? 1400 1200 1000 800 600 400 200 10 20 30 40 O Yes
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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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 = 1400, k = 13, 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?
P
1400
1200
1000
800
600
400
200
10
20
30
40
Yes
No
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