Answered: Suppose that the DE dy = y(90 – y) –…

Suppose that the DE dy = y(90 – y) – 2000 dt models a logistic equation with harvesting, where y(t) represents a tilapia popu lake at time t, measured in years.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.EA: Extended Application Managing Renewable Resources

Problem 1EA: Suppose that a particular plot of land can sustain 500 deer and that the population of this...

See similar textbooks

Related questions

Q: Another equation that has been used to model population growth is the Gompertz15 equation dydt=ry…

Q: Consider a disease where immunity is lost. On average, after n days, a recovered person becomes…

A: Let t be the time ,which is an independent variable (measured in days). We have to take two related…

Q: Match the appropriate slope field with the differential equation y'=+2. 事 B.

A: given differential equation y'=xy2+2 claim- to find the slope field of the given equation definition…

Q: A population is modeled by the differential equation dP = 1.005P1- dt P 7500 For what value(s) of P…

A: The Given Differential equation is: dPdt = 1.005P1-P7500

Q: Find the general solution to the separable differential equation: (2x + 1)(x + 1)y' = - %3D For full…

Q: There is considerable evidence to support the theory that for some species there is a minimum…

A: Given- There is considerable evidence to support the theory that for some species there is minimum…

Q: Which of the following graphs is the solution to the logistic differential equation -(1- with the…

Q: Suppose that a certain population obeys the logistic equation dy/dt = ry(1 − (y/K)). a.If y0 = K/3,…

A: (a)calculation:

Q: Consider the following model for a population that is changing due to births, deaths, immigration,…

Q: A murder of crows in the wild is observed to double its population in one year. However, in…

Q: dy 2. When does the differential equation Cekt represent exponential growth? exponential dt decay?

A: We need to explain growth and decay.

Q: Find: (a) particular solution of the logistic differential equation that describes the growth of…

A: The logistic differential equation that describes the growth of the population of wolves in some…

Q: t sec 0 de dt Oet?

Q: (i) Show that the solution of the logistic equation dr az – br dt (3) is given by 1(t) a – br(t)…

Q: Find the differential equation of the exponential curve y = A(33x) where A is an arbitrary constant.…

Q: The differential equation y' = e3x+Iny is linear and separable. %3D Select one: True False

Q: Find the logistic differential equation dy ky 1-Y dx L

Q: Draw a phase line for the autonomous differential equation and label each equilibrium point as a…

A: We have to draw a phase line.

Q: Write an equivalent first-order differential equationand initial condition for y

A: We have to write an equivalent first-order differential equation and initial condition for y…

Q: Decide if the differential equations whose slope fields are shown below involve only x, only y, both…

A: To Find: Decide if the differential equations whose fields are shown above involves only x, only…

Q: Find the logistic differential equation of dy/dx=ky(1-y/L)

Q: The differential equation dudx=5u+10 admits one equilbrium solution that is asymptotically…

A: The given solution is unstable whose plot is shown below.

Q: dy =ky L) dx

A: We will find the logistic differential equation Where L carring Capacity

Q: Consider the following logistic equation for t20 Sketch the direction field, draw the solution curve…

A: given differential equation P't=0.05P-0.002P2 with initial condition P0=10 , P0=20 , P0=35 claim-…

Q: Is the logistic equation a linear differential equation?

Q: Verify that y(t) = ceat solves the differential equation for unlimited growth, y' = ay, with initial…

A: Given Differential Equation : y1 = ay , y(0) = C i.e. dydt =ayie dyy = adt Integratinh both side we…

Q: Find the general solution of the inhomogeneous equation y" + 3y' = te'.

Q: Find the logistic equation that passes through the given point. dy/dt = 7y/20 - y^2/1140 (0,21)

Q: Classify the given differential equation according to its type, order, degree, and linearity. du…

Q: The ordinary differential equation 2xy" + y = ycosx is linear False O True

A: Given differential equation is 2xy'' + y = ycos(x)

Q: Is the given Differential Equation a homogenous? If yes, what is the degree?

A: We know that a differential equation containing a homogenous function is called a homogenous…

Q: 19.) [(ycoth y² )log°(sinh y² )dy

Q: The differential equation for cooling of a cup of coffee is given by dT dt = -(T – Tenu)/T where T…

A: final answer is T = 200 C at t =5 minutes detailed solution with explanation is given below

Q: Q7 (a) Sketch the phase line for the autonomous differential equation= f(y), where the graph of the…

Q: Identify if the differential is homogenous or heterogeneous. State also whether the equation is…

A: As per guideline we have to solve three subparts

Q: There is considerable evidence to support the theory that for some species there is a minimum…

A: Given: dPdt =-rP1-PK1-PT , P ,t≥0r=0.01 , K=13000 , T= 400 To check where population increases and…

Q: Suppose a population P(t) satisfies logistic differential equation dP/dt=0.1P(1-(P/2000))…

A: SOLUTION-

Q: Suppose that the population of a town is growing continuously at an annual rate of 2% per year.…

A: topic - differential equations dP/dt =0.02P

Q: Consider an interest rate model following the stochastic differential equation: dri = Odt + odW1,…

Q: The dynamics of a fish population is described by the Richard's growth law dN (1) dt where N = N(t)…

A: rN is the part of the equation which signifies the rate of change of population dN/dt. r is the…

Q: Find the function ?(?) that satisfies the differential equation dy/dt - 2ty = -6t2et^2 and the…

Q: A murder of crows in the wild is observed to double its population in one year. However, in…

Q: 2. Consider a logistic equation: dN 2(1 - dt N. with the initial population No = 2. Find the…

Q: The population of a particular type of fish in a lake would grow logistically according to the…

A: The population of lake is given by, dydt=0.03y1−y2800 and y0=1320 To determine the number of fish…

Q: What is the slope field of a differential equation y' = ƒ(x, y)? What can we learn from such fields?

Q: Use Laplace transforms to solve the differential equation y' + 2 y = 10 e3t , if y(0) = 6

A: The given equation is: y'+2y=10e3t,y(0)=6...(1) Taking Laplace transform on both sides of equation…

Q: Show that solving the logistic differential equation results in the logistic growth function

A: The given differential equation is dydt=825y54-y with y0=1. Solve the above differential equation…

Q: Find the logistic equation that passes through the given point. dy/dt = y(1 − y/80), (0, 8)

A: Our Aim is to find the logistic equation that passes through the given point.dydt=y1-y80 and the…

Question

100%

y(t) =
d) The stable critical point is
y =
while the unstable one is
e) Using the fourth order Runge-Kutta Method, with a step-size of h =
1
to approximate
12'
y() if y(0) = 55, yields:
ko1

Suppose that the DE
dy
y(90 – y) – 2000
dt
-
models a logistic equation with harvesting, where y (t) represents a tilapia population in a
lake at time t, measured in years.
a) The per capita growth rate of the tilapia population is
b) The rate at which the tilapia is harvested is
c) The limiting and threshold solutions are, respectively,
y(t) =
and

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Suppose that a particular plot of land can sustain 500 deer and that the population of this particular species of deer can be modeled according to the logistic model as dPdt=0.2(1P500)P. Each year, a proportion of the herd deer is sold to petting zoos. a. Find the function that gives the equilibrium population for various proportions. b. Determine the maximum number of deer that should be sold to petting zoos each year. Hint: Find the maximum sustainable harvest
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?
What is the y -intercept on the graph of the logistic model given in the previous exercise?