Suppose the logistic curve y(t)Lsatisfies that y(0) = 6. What is the1+6e-7tcarrying capacity?4221cannot be found76

Answered: Image /qna-images/answer/8fd0fbd5-9de4-4333-b8bd-0d2d999dd756.jpg

Answered: Suppose the logistic curve y(t) =…

Math

Calculus

Suppose the logistic curve y(t) = satisfies that y(0) = 6. What is the 1+6e-7t carrying capacity?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 15SE: What is the y -intercept on the graph of the logistic model given in the previous exercise?

See similar textbooks

Related questions

Q: for every choice of the constant c, the function x =( K ) / ( 1+ce−rt ) is a solution of the…

Q: Suppose that the DE dy y(70 - y) – 600 dt models a logistic equation with harvesting, where y (t)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: The growth of a new restaurant depends on the number of its regular customers as p'(t) = .05√p(t)…

A: TA differential equation is a equation that connects the derivatives of one or more unknown…

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

Q: The solution of the following logistic equation is dy = ry dt (13-): (0)- k 10

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: The decay is basically governed by the first order differential equation = - ka is

A: We have to identify the given statement as true or false.

Q: (с) гу' + ху — 1— у, у(1) — 0

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: A firm hires 3t% workers each year but loses 5% each year due to retirement and poaching from…

A: topic - differential equation

Q: The solution of the following logistic equation is dy = ry (11 –):y (0) = k %3D dt 13 1 ellrt 144 Y…

Q: Find the general solution of the differential equation: logS=x+y

A: We have given a differential equation , logS = x + y We know that , elog(a) = a . So , elog(S) = ex…

Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

Q: Find the general solution of the logistic equation *- » dy dt = 3y (1 -) n find the particular…

Q: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

Q: If a quantity grows/decays at a rate proportional to its size, its growth can be expressed as dQ/dt…

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: Use exponential shift to find the general solution of the differential equation. (D+1)°y = 0

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

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

Q: Identify the differential equation that produces the slope field below. // ||// // 2.

Q: Obtain the general solution of the Logistic differential equation dP P - p? dt

A: Given Logistic differential equation is dPdt=P-P2 to find the general solution

Q: A certain population is known to be growing at a rate given by the logistic equation = x(b – ax).…

A: Firstly find critical points. After that find second derivative , If second derivative less than…

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: Lake Taal has a volume of 458 cubic km, and its rate of inflow and outflov are both 175 cubic…

Q: To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t)…

Q: Find the order of the differential equation. And check if it is linear or nonlinear.

A: Given the differential equation

Q: Verify that the function y = Ce5x is a solution of the differential equation y′ = 5y

A: The given function is y = Ce5x The differential equation is y′ = 5y

Q: Suppose that the DE dy = y(70 – y) – 600 dt - models a logistic equation with harvesting, where y…

A: The given model of logistic equation with harvesting is, where, y(t) represents the tilapia…

Q: 2 Solvehe initial value problems below. dy dt

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Find the logistic equation that passes through the given point. dy = 1.72y 1 dt (0, 4) - 6 y =

A: We solve the given differential eqn. By method of separable variable

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

Q: y = Ax² + Be*

Q: This problem deals with the differential equation dx/dt kx(x – M) – h that models the harvesting of…

Q: The rate at which radioactive nuclei decays is proportional to the number of such nuclei that are…

A: Given Half of the original number of radioactivenuclei have undergone disintegration in a period of…

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: The solution of the following logistic equation is dy - ry (7 –);y(0) k dt 15 1 -e7rt 105 y – 7k 1…

A: Given

Q: 5. Verify that y = (x³ – x) log cx satisfies the differential equation (x³ – x)y' – (3x? – 1)y = x5…

Q: On the early detection period of COVID-19, there were 557 people verified to have been infected by…

A: Given, Number of patients initially=557 The rate of increase of patient is given by,…

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

A: SOLUTION-

Q: The total number of reported cases of an illness in a large city days after the start of an outbreak…

A: According to the given information the total number of reported cases of an illness in a large city…

Q: Can you please verify that the given two-parameter family of functions is the general solution of…

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

Q: A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the…

A: Please check step 2 for the solution.

Q: Find the solution y(t) by recognizing the differential equation as determining unlimited, limited,…

Q: dy - r (11 - 2) : v(0) = ; k (11–);y (0) dt 9

A: dy/dt = ry (11-y/k) integration (1/y(11-y/k)dy) = integration (rdt) R.H.S. integration (rdt) = rt+C…

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…

Question

Suppose the logistic curve y(t)
L
satisfies that y(0) = 6. What is the
1+6e-7t
carrying capacity?
42
21
cannot be found
7
6

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Systems of Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

What is the y -intercept on the graph of the logistic model given in the previous exercise?
The natural logarithmic function f(x)=Inx has the ____________ asymptote x =____.
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?
Use the result from the previous exercise to graph the logistic model P(t)=201+4e0.5t along with its inverse on the same axis. What are the intercepts and asymptotes of each function?
What is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?
To the nearest whole number, what is the initial value of a population modeled by the logistic equation P(t)=1751+6.995e0.68t ? What is the carrying capacity?
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
The population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t where t is in
The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.
The natural logarithmic function f(x)= In (x1) has the ____________ asymptote x =____.
Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .