The population of a community is known to increase at a rate proportional to the number of peoplepresent at time t. If the initial population Po has doubled in 5 years, determine how long will it taketo triple? To quadruple?Solve the above population problem as follows:a) construct a linear first-order Differential Equation (DE) that models the behaviour of thepopulation growth with initial condition;b) solve the DE and find the constant k using the fact that the population doubles in 5 years;c) using the answer in (b), find the value of t, when the population triples;d) using the answer in (b), find the value of t, when the population quadruples;

Answered: Image /qna-images/answer/7e3d780b-efe1-4122-8af3-bb12a16d161b.jpg

Answered: The population of a community is known…

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 colony of 120 wood frogs was introduced to a pond with a carrying capacity of C=300. The population grows according to the logistic growth model, with a growth parameter is r = 1.5. The logistic growth formula is: pN+1 = rpN(1-pN) a) Find the initial p-value: p0 = Answer b) Find the first p-value: p1 = Answer c) Find the second p-value: p2 = Answer
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.
(c) Describe a scenario in which you are modeling the growth rate of a population, but the differential equations in the previous two parts (the Malthusian Growth Law and Lo- gistic Growth Law respectively) might not be appropriate. Then give a differential equation which models your sce- nario. Be creative, and don't use the equation we used in class!
A and B can do a piece of work in 12 days; B and C can do it in 15 days while C and A can finish it in 20 days. In how many days will A,B,C finish it, working togeteher? In hpw many days will each one of them finish it, working alone?
B. Solve the problems related to the application of First Order Differential Equations. 3. Continuous Compound Interest If $150 is deposited in bank that pays 51% annual interest compounded continuously. Find the value of the account after 10 years.
In 30 min
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

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