During the period from 1790 to 1910, a country's population P(t) in years) grew from 3.7 million to 84.7 million. Throughout this period, P(t) remained close to the solution of the initial valuedPproblem = 0.03144P -0.0001486P², P(0) = 3.7.dt(a) What 1910 population does this logistic equation predict?(b) What limiting population does it predict?(c) The country's population in 2000 was 310 million. Has this logistic equation continued since 1910 to accurately model the country's population?

Given differential equation is: At the year 1910, the population is million.To find:a) Population…

Answered: During the period from 1790 to 1910, a…

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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At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.) 20 y = dy dt = 1 +9e 8 g (c) When will the culture's weight reach 16 grams? (Round your answer to two decimal places.) 9.79 hr (d) Write a logistic differential equation that models the growth rate of the culture's weight. Then repeat part (b) using Euler's Method with a step size of h = 1. (Round your answer to the nearest whole number.) y(5) = 6 -0.3662t = 1.37 0.366y| 1 (1-20) (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) X g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.) hr
Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 5000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP = kp (1-P). (1-²), kP dt determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k= P(t)= (b) How long will it take for the population to increase to 2500 (half of the carrying capacity)? It will take years.
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?
In a chemical reaction, the rate is dependent on the concentration of reactants raised to a power. What is this power known as ? A) Rate constant B) Reaction order C) Activation energy D) Catalyst
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

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