Mathematical ModelingSuppose a population satisfies a logistic model where r = 0.4, K = 100, x (0) = 5. Find the population size for t = 10. Question 5: Suppose a population satisfies a logistic model with r = 0.4, K = 100,x(0) = 5. Find the population size for t = 10.dxdtx(1-²)Krx

5. Given that the population satisfies a logistic model with r=0.4, K=100, x0=5 Also given dxdt=r…

Answered: Question 5: Suppose a population…

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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Variable Intercept x1 X2 Variable X₁ X2 LPM -0.30 (0.03) 0.27 (0.06) -0.05 (0.02) a. At the 5% significance level, comment on the significance of the variables for both models. x₁ = 10, X₂ = 14 x₁ = 10, X₂= 25 Logistic -2.50 (0.03) x₁ = 10, x₂ = 14 X₁ = 10, x₂ = 25 LPM Not significant Significant 1.03 (0.07) b. What is the predicted probability implied by the linear probability model for x₁ = 10 with x2 equal to 14 and 25? Note: Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places. Report the probability between 0 and 1 (not in %). ŷ -0.30 (0.01) у Logistic Not significant Significant What is the predicted probability implied by the logistic model for x₁ = 10 with x2 equal to 14 and 25? Note: Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places. Report the probability between 0 and 1 (not in %).

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Question 5: Suppose a population satisfies a logistic model with r = 0.4, K = 100, x(0) = 5. Find the population size for t = 10. dx dt ·x (1 – ²) =rx