A population tries to grow exponentially but is limited by the resources of its environment. This growth ismodeled by the differential equationdP kdt= -P(M-P).MFind a solution for this differential equation using the continuous growth rate k = 0.3, the carryingcapacity M = 20, and the initial population size P(0) = 4.P(t) =Hint: You can solve the differential equation using separation of variables, but the calculations may beeasier if you treat it as a Bernoulli equation.

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Answered: A population tries to grow…

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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-Kipped par Tutorial Exercise A population of a particular yeast cell develops with a constant relative growth rate of 0.4985 per hour. The initial population consists of 3.2 million cells. Find the population size (in millions of cells) after 3 hours. Step 1 dP = 0.4985P dt 0.4985P Since the relative growth rate is 0.4985 per hour, then the differential equation that models this growth with P in millions of cell and t in hours is Step 2 We know that P(t) = P(0)ekt, where P(0) is the population on day zero and k is the growth rate, Substitute the values of P(0) and k into P(t) (in millions of cells). P(t) = P(0)ekt million cells 7.1856 million cells Submit Skip (you cannot come back) Need Help? Read It
A): What is the carrying capacity of the population? B): What is the total population at the moment the population is growing at the fastest rate? Please find part A and B
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 30 min
a continuing increase of the population on Earth eventually encourages settlement of the moon and mars. After colonization of the moon and mars, births rates continue to exceed death rates on earth, but life is hard away from earth so that the opposite is true elsewhere in the solar system. Nonetheles, the rising earth population constantly relocates the moon and Mars depending on the relative differences in population sizes. You have modelled the population dynamics via the following differential equations, where X1(t) is the Earth population at time t, X2(t) is the moon population, a and X3(t) is the population on mars. x`1 = -3/2 (x1-x2) - (x1-x3) + 3/2 x1 x`2 = -1/2 (x2 -x1) - 1/2(x2 -x3) - x2 x`3 = -1/2 (x3 -x1) - 1/2 (x3 -x2) - 1/2x1 a) if at time t=0 there are five bilion people on earth , and no one on moon and mars, Whats the population distribution far in the future? b) suppose instead that at a time t=0, 5/3 bilion people were on the moon, leaving 10/3 bilion on earth,…
Part d please
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
A tank originally contains 120 litre of brine with a salt concentration of 4 gram of salt per litre. Then brine with 15 gram of salt per litre is poured into the tank at a rate of 6 litre/minute, and the well-stirred mixture is allowed to leave at the same rate. a. Model this situation by a differential equation with initial conditions. b. Find the concentration of salt in the tank after 20 minutes. c. Find the eventual concentration of salt in the tank. (Hint: The eventual value will be as time goes to infinity.)
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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