Consider the logistic equation(a) Find the solution satisfying y₁ (0) = 8 and y/₂(0) = -5.yi(t) = 8Y2(t)(b) Find the time t when y(t) = 4.t=(c) When does y2 (t) become infinite?t=

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Answered: Consider the logistic equation (a) Find…

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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9. Solve the following simultaneous equations: logx+log(y²)=4 log²x-3log(xy) = -5 Where x, y are real numbers
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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During the period from 1790 to 1920, a country's population P(t) (t in years) grew from 3.6 million to 101.6 million. Throughout this period, P(t) remained close to the solution of the initial value problem -0.0001494P² P(0) = 3.6. dP dt = 0.03136P-( (a) What 1920 population does this logistic equation predict? (b) What limiting population does it predict? (c) The country's population in 2000 was 259 million. Has this logistic equation continued since 1920 to accurately model the country's population? (a) The logistic equation predicts the population in 1920 to be million. (Do not round until the final answer. Then round to the nearest thousandth as needed.) K AI C H TU U →> C ¢ ➡ H i O + 2.4 e В → نه Y + - 8 .... : *** 5 Ø Co Less . N 0 .. H A E X U i 9 A C ש Σ VI 8 FR > in X
An observation indicates that the initial population of grey seals P(t) nearby a harbor is 25 and satisfies the logistic equation P(t)' = 0.0225P(t) - 0.0003P(t)² (with t in months.) a) Apply Euler's method together with any computer program (compulsory) to approximate the solution for 10 years. Use the step size of h = 1 and then with h = 0.5. (LT-C3) b) Find out the percentage of the limiting population of 75 grey seals has been attained after 5 years and after 10 years. (LT-C2) c) Summarize your findings in (b). (LT-C4)

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Consider the logistic equation (a) Find the solution satisfying y₁ (0) = 8 and y/₂(0) = -5. yi(t) = 8 Y2(t) (b) Find the time t when y(t) = 4. t= (c) When does y2 (t) become infinite? t=