A population is modeled by the logistic differential equation:\[ P'(t) = 2P \left( 1 - \frac{P}{2000} \right). \]1) What are the equilibrium solutions?2) Let \( f \) be the solution satisfying the initial condition \( f(0) = 3000 \). Is \( f \) an increasing function or decreasing function?3) What is \(\lim_{t \to +\infty} f(t)?\)

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The population of an aquatic species in a certain body of water is approximated by the logistic function 37,500 where t is measured in years. Find G(t) = = ,-0.56t' the population and its growth rate at the following times. a. 1 year b. 5 years c. 12 years d. What happens to the rate of growth over time? 1 + 12e The population in 1 year is 4774 . (Round to the nearest whole number.) The population in 5 years is 21680. (Round to the nearest whole number.) The population in 12 years is 36965. (Round to the nearest whole number.) The growth rate in 1 year is per year. (Round to the nearest whole number.)
I have tried 8 percent, 0.080, 0.079, and many others however I am still stuck on this problem. I even tried a different method that gave me 11.82 still wrong.
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38. Given the power regression model y = 40x^1.3, which is the linear regression model after transforming to a log-log graph? Y = 1.3X + 1.60 Y = 0.20X + 0.11 Y = 0.20X + 0.36 Y = 1.60X + 0.11
plot the data points and find a logistic model of the form P(t) - c/1+a*e^-bt what is the value of c and what does c represent year population 1700 .6 1803 1 1928 2 1950 2.5 1960 3 1987 5 2019 7.7 2050 9.7 2100 10.9
During the period from 1790 to 1930, a country's population P(t) (t in years) grew from 3.7 million to 118.6 million. Throughout this period, P(t) remained close to the solution of the initial value dP problem = 0.03145P-0.0001486P², P(0) = 3.7. dt (a) What 1930 population does this logistic equation predict? (b) What limiting population does it predict? (c) The country's population in 2000 was 350 million. Has this logistic equation continued since 1930 to accurately model the country's population?
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A population is modeled by the logistic differential equation P P'(t) = 2P(1. 2000 1) What are the equilibrium solutions? -