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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Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 8100. The number of fish doubled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP - kp(1-2). = 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 4050 (half of the carrying capacity)? It will take 3.575 years.
A population grows according to the logistic growth model, with growth parameter r= 1.8. Starting with an initial population given by P = 0.6, complete parts (a) and (b). (a) Find the values of p₁ through P10- P₁ = ₁ P₂ = P3 = P4 = P5 P10 = P6= P7 = ₁ P8 = Pg = ₁ (Round to four decimal places as needed.) (b) What does the logistic model predict in the long term for this population? O A. The population settles into a two-period cycle with the following approximate percentages of the habitat's carrying capacity: 44.17% and 44.43%. OB. It stabilizes at about 44.44% of the habitat's carrying capacity. C. The species will become extinct. OD. The population settles into a four-period cycle with the following approximate percentages of the habitat's carrying capacity: 44.17%, 44.43%, 43.20%, 44.44%.
Hello! How do you solve part (a), (b), and (c) of the question attached below? Thank you for your help! Have a nice day :)
The population of Nevada was 3.0 million in 2018 and 2.7 million in 2010. Assuming an exponential model: (a) Write the population of Nevada in the form N= Noat, where N is the population of Nevada in millions, No and a are constants, and t is time in years since 2010. NOTE: Enter the exact answer for No. Enter an exact value for a or round to 4 decimal places. N (t): - (b) What was the estimated population of Nevada in 1996? NOTE: Round your answer to 3 decimal places. The population in 1996 was approximately million people.
A certain phenomenon has an initial value of 12 and grows at a rate of 8% per year. Give an exponential function N = N(t) that describes this phenomenon. (Use t in years as your variable.)
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?
1 t
2. Solve the equations a. ( b. ( b. ( ) e²x - 7e-8 = 0. ) 2(3x+6)_8(1-x) = 0. ) log (x)+ log (x - 6) = 1.

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