2. (Population Logistic Model) Let P(t) represent the population of a certain species at time t.The following IVP describes the growth/decay of the populationdP = TP (1-P). P(0) = PodtKwhere r is the population growth/decay rate, and K is the population carrying capacity.Consider the values Po = 50, K = 300, r = 0.1.a. Find the equilibrium population(s).b. Solve the IVP. Then, compute P(16). Remark. Solve the DE as a Bernoulli DE.c. Find the limiting population and give a physical interpretation to your finding.d. Sketch the population curve versus time showing your findings in Parts b and c.

The main objective is to solve the population logistic model. As per our guidelines I, allowed to…

Answered: (Population Logistic Model) Let P(t)…

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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5. The rate of change in revenue for the Priceline Group from 2004 to 2013 can be modeled dR by = 0.07e0.2387t where R is the revenue (in billions of dollars) and t is the time (in dt years), with t=4 corresponding to 2004. In 2013, the revenue for the Priceline Group was $6.8 billion. a. Find a model for the revenue of the Priceline Group b. Find the revenue of the Priceline Group in 2012.
The type of battery in Jim's laptop has a lifetime X (in years) which follows a Weibull distribution with parameters α=2 and β=4. The type of battery in Jim's tablet has a lifetime Y (in years) which follows an exponential distribution with parameter λ=1/4.Find E(XY−2Y).(Answer as a decimal number, and round to 2 decimal places).
A population of fish is living in an environment with limited resources. This environment can only support the population if it contains no more than M fish (otherwise some fish would starve due to an inadequate supply of food, etc.). There is considerable evidence to support the theory that, for some fish species, there is a minimum population m such that the species will become extinct if the size of the population falls below m. Such a population can be modelled using a modified logistic equation: dP =(1-)(-) m dt M
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Suppose that the equation dr = kr(M – 1) – Er dt models the population of fish in a lake, where harvesting occurs at the rate of Ex fish per month (E a positive constant call harvesting effort). If 0 < E < kM, (a) If 0 < E < kM, show that the population is logistic. (b) What is the limiting population? kM (c) Show that the maximum sustainable harvesting effort is Emax 2 (d) If E 2 kM, show that r(t) → 0 as t → x, that is the lake is eventually fished out.
Find the linearization L(x) of the function at a. f(x) = x2/3, a = 64 %3! L(x) =

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