A state game commission releases 50 elk into a game refuge. After 5 years, the elk population is 110. The commission believes that the environment can support no more than 4200 elks. The growth rate of the elk population P is modeled by the logistic differential equation dP = kP(1- P/4200 ), 50 ≤ P ≤ 4200, where t is time in years. (a)Use the logistic equation P = L/(1+be^(-kt)) to write a model for the elk population in terms of time t by finding the values for b and k. (b) Use the model to estimate the elk population after 20 years.
A state game commission releases 50 elk into a game refuge. After 5 years, the elk population is 110. The commission believes that the environment can support no more than 4200 elks. The growth rate of the elk population P is modeled by the logistic differential equation dP = kP(1- P/4200 ), 50 ≤ P ≤ 4200, where t is time in years. (a)Use the logistic equation P = L/(1+be^(-kt)) to write a model for the elk population in terms of time t by finding the values for b and k. (b) Use the model to estimate the elk population after 20 years.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
Related questions
Question
A state game commission releases 50 elk into a game refuge. After 5 years, the elk population is 110. The commission believes that the environment can support no more than 4200 elks. The growth rate
of the elk population P is modeled by the logistic differential equation dP = kP(1- P/4200 ),
50 ≤ P ≤ 4200, where t is time in years.
(a)Use the logistic equation P = L/(1+be^(-kt)) to write a model for the elk population in terms of time t by finding the values for b and k.
(b) Use the model to estimate the elk population after 20 years.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage