Suppose that a population grows according to a logistic model with carrying capacity 5700 and k = 0.0016 per year. (a) Write the logistic differential equation for these values. 0.0016P(1-5700) dp dt
Suppose that a population grows according to a logistic model with carrying capacity 5700 and k = 0.0016 per year. (a) Write the logistic differential equation for these values. 0.0016P(1-5700) dp dt
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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Question
![(c) Use Euler's method with step size h= 1 to estimate the population after 50 years if the initial population is 1,000. (Round your answer to the nearest whole number.)
P(50) -
(d) If the initial population is 1,000, write a formula for the population after t years. (Use P for P(t).)
5700
1+4.9e-0.0016 X
P=
Use it to find the population after 50 years and compare with your estimate in part (c). (Round your answer to one decimal place.)
P(50) -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3c956df-0a2d-423a-9ad6-9040740ddec6%2F92661fad-6e5b-4860-a43d-7b427b41e939%2Fendiwgv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(c) Use Euler's method with step size h= 1 to estimate the population after 50 years if the initial population is 1,000. (Round your answer to the nearest whole number.)
P(50) -
(d) If the initial population is 1,000, write a formula for the population after t years. (Use P for P(t).)
5700
1+4.9e-0.0016 X
P=
Use it to find the population after 50 years and compare with your estimate in part (c). (Round your answer to one decimal place.)
P(50) -
![Suppose that a population grows according to a logistic model with carrying capacity 5700 and k = 0.0016 per year.
(a) Write the logistic differential equation for these values.
0.0016P(1-
dP
dt
-
5700](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3c956df-0a2d-423a-9ad6-9040740ddec6%2F92661fad-6e5b-4860-a43d-7b427b41e939%2Fv0qan3t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that a population grows according to a logistic model with carrying capacity 5700 and k = 0.0016 per year.
(a) Write the logistic differential equation for these values.
0.0016P(1-
dP
dt
-
5700
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