number of people who will be infected by t =12 days.7. Assume we are considering the survival of whales and that if the number of whales fallsbelow a minimum survival level m, the species will become extinct. Assume also thatthe population is limited by the carrying capacity M of the environment. That is, if thewhale population is above M, then it will experience a decline because the environmentcannot sustain that high a population level.a. Discuss the following model for the whale populationdPdt= k(MP)(Pm)where P (t) denotes the whale population at time t and k is a positive constant.b. Graph dP/dt versus P and P versus t. Consider the cases in which the initialpopulation P(0) = Po satisfies Po

The model for the whale population is given by dPdt=kM-pp-m where p is the population of whale at…

Answered: 7. Assume we are considering the…

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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1. The population of Normal, Illinois grows proportionally to its population at time t. At an initial population of 1500, it grows at a rate of 12% over 9 years. What is the value of the proportionality constant?a. 0.01259/yrb. 0.004435/yrc. 0.004856/yrd. 0.00767/yr 2. What is the population of Normal, Illinois in 30 years?a. 2188 peopleb. 3655 peoplec. 2643 peopled. 5553 people 3. A sample of organic origin was tested to determine its approximate age. About 52% of its C-14 had decayed. Use a half life value of 5730 years to determine how old the sample is.a. 6067.37 yearsb. 11,136 yearsc. 8219 yearsd. 17,527 years 4. A prehistoric artifact was recently found off the coast of Borneo. Based on carbon dating, approximately 88% of the C-14 remained. Use the half-life of C-14 as 5,730 years. What is the approximate age of the artifact?a. 1057 yearsb. 2489 yearsc. 5406 yearsd. 3819 years 5. A 400-L tank initially contains 40 kg of KCl. There is an incoming flow rate of 8 L/min of a 2 kg…
The Lotka-Volterra equations are often used to model the links between a particular population of prey organisms and a population of predatory organisms. In a particular ecosystem u is used to represent the number of predatory organisms and v to represent the number of prey organisms. Suppose the growth rate uv of the predatory organisms is f(u,v) = - 0.5u + and of the prey organisms is g(u,v) = 6v – 10uv. 100 (a) Show that if u = 0.6 and v = 50, then f (u,v) = 0, and g(u,v) = 0. (The populations are said to be in equilibrium.) %D %3D f(u,v) (b) Find the linear approximation of the vector valued function h:(u,v)→ if u is close to 0.6 and v is g(u,v) close to 50. (a) Evaluate f(u,v) at u = 0.6 and v = 50, f(0.6, 50) = (Type an integer.)
Q No. 2: Five people in a community with stable population of 5000 people got infected with a contagious disease (such as covid 19). A theory of epidemic spread postulates that the rate of change in the infected population (number of people) is proportional to the product of the number of people who have the disease with the number that are disease free (take the constant of proportionality as 6.0 x 104). Assuming the theory is correct, how long will it take 75% of the population to contract the disease? (Assume the community as a closed system with nobody goes out or comes in but they are free to meet each other).
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
A stirred-tank blending system initially is full of water and is being fed pure water at a constant flow rate, q. At a particular time, an operator adds caustic solution at the volumetric but concentration cj. If the liquid volume V is constant, the dynamic model for this flowrate process is: dc V + gc = qc{ dt with c(t = 0) = 0. a. What is the concentration response of the reactor effluent stream, c(t)? b. Sketch it as a function of time. Use the following data: V= 2 m³, q = 0.4 m³/min, c; = 50 kg/m³
Suppose the number of bacteria in a culture increases by 50% every hour if left on its own. Assuming that biologists decide to remove approximately one thousand bacteria from the culture every 10 minutes, which of the following equations best models the population P = P(t) of the bacteria culture, where t' is in hours? A. dP = 5P-1000 dt dP B. at dP C. dt dP D. dt E. dP at = 5P-6000 1.5P-6000 = 1.5P-1000 = -5P-1000
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.

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