Suppose that at time t =0, half of a “logistic” population of 100;000 persons have heard a certain rumor, and that the number of those who have heard it is then increasing at the rate of 1000 persons per day. How long will it take for this rumor to spread to 80% of the population? (Suggestion: Find the value of k by substituting P(0) and P'(0) in the logistic equation,

Q: Assuming P≥0,, suppose that a population develops according to the logistic equation…

A: Given. We are given the rate of change of population of any species with respect to time and it is a…

Q: During the period from 1790 to 1930, the U.S. population P(t) (t in years) grew from 3.9 million to…

A:

Q: Given the exponential growth function f(x) = 78(1.0145)* What is the initial value of the function?

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Q: An observation indicates that the frog population Q(t) in a small pond is 25 initially and satisfies…

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A: Given, N=K1+be-rt Where  the constant K represents carrying  capacity and b is, b=KN0-1 Then, the…

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A:

Q: Consider the following. 150 P(t) 1 + 6.655e-0.68t To the nearest whole number, what is the initial…

A: The given population model,     P(t)=1501+6.655e-0.68t

Q: Suppose that the growth-rate parameter k = 0.3 and the carrying capacity N = 2500 in the logistic…

A: Given that, The growth-rate parameter k = 0.3. The carrying capacity N = 2500. Suppose P(0) = 2500.…

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A:

Q: You have 500-grams of an unknown radioactive substance that has been determined to decay according…

A: D(t) = 500e-0.001904.tLet substance take x years to become half of the initial ammount.After x years…

Q: A group of survivors on a supply run has returned to their base camp with a population of 2000. Two…

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

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A:

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A: Given that Nt represents the number of people who are exposed to a particular advertisement. The…

Q: 4) The student population at a certain school here in Dagupan can be modeled by the logistic growth…

A: You must have idea about growth model to understand it better.

Q: You are asked to find the value of a certain number associated with the logistic formula K N = 1+ be…

A: initial population means at t=0 . given that:- N0=279 , b=8 ,t=0

Q: Suppose $2000 is invested at 7% interest compounded continuously. How long will it take for the…

A: Given query is to find the time taken to reach the investment of 2000 to 10000 if compounded…

Q: In the logistic model, N = 0 is a stable equilibrium point when ... а. r>0 O b. K>0 Ос r not equal…

A: The equilibrium point of a differential equation is the point where the rate of change is zero. For…

Q: Suppose there is one pupil in a class of 60 who was infected by the Influenza B virus. Assuming none…

A: We will solve the problem using the concept of logistic growth .

Q: The population of a culture of bacteria is modeled by the logistic equation P(t) = 14,250/ 1 + 29e…

A: P(t) = 14,250/ 1 + 29e -0.62t   Initial population When t=0, P(0) = 14,250/ 1 + 29 =475 Therefore,…

Q: A Population of Dogs can be modeled by the Logistic curve 40 P(t)= 1+7e-0.03€ Where t is time in…

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Q: Write the solution of the logistic initial-value problem   dP/dt = 0.00008P(1000 - P)   P(0) = 100…

A: The logistic initial-value problem dPdt=0.00008P1000-P, P(0)=100. We have to find the population…

Q: Suppose there is one pupil in a class of 60 who was infected by the Influenza B virus. Assuming none…

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Q: Solve the following equation for x: log3(ln(x)) = 2.

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Q: Suppose the population of a city is modeled by the logistic equation dP dt P, 100 P(0) = 1 Use…

A: Given :

Q: Suppose that a population develops according to the logistic equation dP = 0.2P – 0.0005 P² dt |…

A: NOTE: Refresh your page if you can't see any equations. . factor out 0.2P

Q: 3. Suppose that daily data was collected on a bacterial population and the following logistic model…

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Q: Suppose that you want to have a $50,000 retirement fund after 40 years. How much will you need to…

A: Given query is to find the investment amount so that can give $50000 after 40 years.

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Q: The logistic growth function f(t) = - describes the number of people, f(t), who have become ill with…

A: Topic = Algebra

Q: Suppose there is one pupil in a class of 60 who was infected by the Influenza B virus. Assuming none…

A: We will find out the required value.

Q: Hello! How do you solve part (a), (b), and (c) of the question attached below? Thank you for your…

A:

Q: Suppose a population is growing according to the logistic formula  N = 550/1.75e-0.41t +1  where t…

A: The logistic formula for the growth of the population is N=5001.75e-0.41t+1

Q: $4,000 is invested with a 5.3% APR compounded continuously. What is the value of the investment…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: The population of a culture of bacteria is modeled by the logistic equation   P (t) = 14,250 / 1+29e…

A:

Q: Consider the following regression equation: log Yni = log 3.07 + 0.9 log X1i + 1.41 log X2i a.…

A: Given, The regression equation is, log Yni = log 3.07+0.9 log X1i+1.41 log X2i

Q: Suppose the deer population P(t) in a small forest satisfies the logistic equation dP 0.0225P –…

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Q: It is expected in traditional mathematics that when you input data into a well-defined equation you…

A: As per the question we are given the logistic equation : xn+1 = f(xn) = rxn(1-xn) And we have to…

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A:

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A: The logistic equation is given as dNdt=Na-bN and its solution is given as N(t)=aN0bN0+a-bN0e-at…

Q: a) A colony of 1000 rabbits lives in a field that can support 5000 rabbits. After one month, the…

A: We are given the following information. The colony has carrying capacity M = 5000. The initial…

Q: The logistic growth equation is represented by the equation: dN Nrmox (1-7) dt =

A: Introduction: There are many different types of population models. All the models are based upon the…

Q: Under certain assumptions of limitations to population growth, the population P (in billions) of the…

A: Topic - derivative

Q: 1 The solution of the equation Log(-z + 2) = i2n is 4

A: (c) 1+i,1-i,-1-i,-1+i is correct. We have to solve the given equation, that is, Log14z4+2=i2π…

Q: 10) The following logistic function model the population P of a koi pond over x months. 68 P(x) =…

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Q: A person places $123 in an investment account earning an annual rate of 2.8%, compounded…

A: Explanation and solutions is given below....

Q: 1. The human population of a certain island satisfies the logistic law dx = kx - dt with k = 0.03…

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Q: If the optimum yield level is 800 and the initial population is 400, find the value of b associated…

A: Given K = 800 N(0) = 400

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.