3. Suppose that daily data was collected on a bacterial population and the following logistic model was found: Xn+1 = 2.01X, – 0.0062X,?. a. According to this model, what is the carrying capacity (maximum sustainable population) for this population? b. Given an initial population size of 50 cm², use the model to predict the population for years 1, 2 and 3.

3. Suppose that daily data was collected on a bacterial population and the following logistic model was found: Xn+1 = 2.01X, – 0.0062X,?. a. According to this model, what is the carrying capacity (maximum sustainable population) for this population? b. Given an initial population size of 50 cm², use the model to predict the population for years 1, 2 and 3.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population…

Q: Suppose in a certain region there are 4,000 bee hives that are threatened by African bees. Initially…

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

Q: A population follows a logistic DDS given by a) Determine the growth rate r. Pa =…

Q: b2-0.62 ar

Q: Assume a simple logistic regression model for X and binary response Y. The estimated parameters are…

A: Introduction: The response variable is Y, which is a binary variable. Suppose it’s two possible…

Q: At a suburban high school, information spreads by word of mouth according to the logistic function…

A: We are given an logistic function Here k is the growth rate and t is the time. Observe from the…

Q: (a) Assume that the carrying capacity for the US population is 800 million. Use it and the fact that…

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: EXERCISE 15. In 2000 Census the U.S. population was estimated to be 281, 000, 000. Suppose in that…

A: Initial Population= 281,000,000 births per year = 3,900,000 deaths per year = 3,200,000

Q: 3. Log-linearize the equation, x, +a = (1-b)

Q: Recall that the logistic model can be written in the form Pn+1 = b Pn- a p a) Give the formulas for…

A: The standard logistic function is defined by the equation, P=L1+Be-rt . Here, N is the carrying…

Q: The natural resources of an island limit the growth of the population to a limiting value of 4,526.…

Q: Recall that the logistic model can be written in the form a) Give the formulas for finding the…

Q: Consider the following model: log(wage,) = Bo+B,educ; +B2exper;+B3exper +u; Suppose that B2=0.08 and…

A: Given: logwagei = β0 + β1educi + β2experi + β3experi2 + uiβ2 = 0.08 ; β3 = -0.001Where, i stand for…

Q: A factory produces two types of tyres. In an experiment in the working life of these tyres the…

Q: 0.232 (or Consider a population of deer, with Po= 889,060, carrying capacity K = 1,022,419, and…

A: Logistic population growth model ⇒dPdt=rP1-Pk

Q: Assume that the population of a city satisfies the logistic hypothesis: "The rate of change of…

A: Let the year 1960 is denoted by t=0.Therefore year 2000 is denoted by: t=40Let the population at…

Q: Biologists release two otters (a type of water animal) into a river. They believe that the river…

A: Detailed explanation:Part i: Finding α and βGiven:Carrying capacity K=500Intrinsic growth rate…

Q: Consider two populations that can be modeled by the logistic equation with the same carrying…

A: We are given two population modeled by logistic equations having same carrying capacity but…

Q: A new town was incorporated in 1960. The size of the town's population was recorded every 5 years…

A: Introduction: Simple linear regression model: A simple linear regression model is given as y^ = b0…

Q: Suppose that you decide to fit a logistic regression model using these data. Let Y = 1 if a subject…

A: From the above information: Estimate Std. Error z-value Pr(>|z|) Intercept -1.88067…

Q: Assume there is a certain population of fish in a pond whose growth is described by the logistic…

A: As per the question we are given the logistic growth model for a fish population. And we have to…

Q: Q 1. The RMU community of 3,000 people is homogeneously mixed. Assume that one person (staff or…

A: Given the mathematical model which tell us the number of people who have contracted the disease…

Concept explainers

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.

Question

3. Suppose that daily data was collected on a bacterial population and the following logistic model was found:
Xn+1 = 2.01Xn – 0.0062X,?.
a. According to this model, what is the carrying capacity (maximum sustainable population) for this
population?
b. Given an initial population size of 50 cm?, use the model to predict the population for years 1, 2 and 3.

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 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

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

Similar questions

Assuming a carrying capacity for world population K = 15 billion, and a population of 7.75 billion as of 2020, estimate the year when population will reach 12 billion, assuming a logistic growth curve applies and with a current growth rate ro = 1.1% per year. What will the updated growth rate rf be in that future year when population reaches 12 billion?
Table 4.18 shows estimated effects for a fitted logistic regression model with squamous cell esophageal cancer (1 = yes, 0 = no) as the response variable Y. Smoking status (S) equals 1 for at least one pack per day and 0 other- wise, alcohol consumption (A) equals the average number of alcoholic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites. A. To describe the race-by-smoking interaction, construct the prediction equation when R = 1 and again when R = 0. Find the fitted YS conditional odds ratio for each case. Similarly, construct the prediction equation when S = 1 and again when S = 0. Find the fitted YR conditional odds ratio for each case. Note that, for each association, the coefficient of the cross-product term is the difference between the log odds ratios at the two fixed levels for the other variable. B. In Table 4.18, explain what the coefficients of R and S represent, for the coding as given above. What hypotheses do the P -values refer to for…
a) Logistically, the growth of Mrs. Fields cookies in different states is closely modeled after this: 19440 P(t) = 1 + 485 e -0.4444t P(t) is number of U.S. cities with a Mrs. Fields cookie storet years after the year 2000, and t is time in years after the year 2000. Use this logistic model to find the number of cities that had a Mrs. Fields cookie store in the year 2000, when they first opened. U.S. cities in the year 2000. b) How many U.S. cities had a Mrs. Fields cookie store in the year 2015. (round to the nearest whole number) U.S. cities in the year 2015.
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
The table shows the yield (in bushels per acre) and the total production (in millions of bushels) for com in a country for selected years since 1950. Let x represent years since 1900. Find a logarithmic regression model (y= a + b In x) for the yield. Estimate the yield in 2020. The regression model is y=+nx. (Round to one decimal place as needed.) The estimated yield in 2020 is bushels/acre. (Round to the nearest integer) Year 1950 1940 1970 1980 1990 2000 2010 *8828889 50 60 70 90 100 110 Yield 37 51 82 98 117 134 153
Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 5000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP = kp (1-P). (1-²), kP dt determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k= P(t)= (b) How long will it take for the population to increase to 2500 (half of the carrying capacity)? It will take years.
In terms of the model parameters, state the null hypothesis that, after controlling for sales and roe, ros has no effect on CEO salary. State the alternative that better stock market performance increases a CEO’s salary.
Consider the following estimated model, where the dependent variable is the log of the hourly wage: log(wage) = 0.417 - 0.238female + 0.17educ + 0.0232 exper - 0.00058exper? +0.0295tenure – 0.00059tenure? female 1 if the person is female, and 0 if the person is male educ = level of education, in years exper = level of expertise, in years tenure = duration of tenure, in years Given that the above regression model has 313 observations, then its degrees of freedom is equal to For the same levels of education, expertise, and tenure, women earn exactly % less compared to men, holding other factors fixed.
The following data gives the approximate population of the world for selected years from 1850 until2000. Year 1850 1900 1950 1980 2000 Population 1.3 (billions) 1.6 3 4.4 Assume that the population growth can be modeled with an exponential function p = bemx where x is the year and p is the population in billions. Use linearleast-squares regression to determine the constants b and m for which the function best fits the data. Use the equation to estimate the population in the year 1970.
You are an econometrician working in the Ministry of Finance in Trinidad and Tobago and using a database consisting of 108 monthly observations on automobile accidents for Trinidad and Tobago between January 2011 and December 2019, you estimate the following model: log( totacc,) = B, + Bit + B2feb, + ßzmar.. + B12dec, + µe where totacc is the total number of accidents, t is time (measured in months), and feb,, mar,, dec, are dummy variables indicating whether time period t corresponds to the appropriate month. You obtain the following OLS results: Number of obs F( 12, Prob > F df 108 31.06 0.0000 0.7969 Source I MS 95) Model | 1.00244071 Residual | .255496765 12 .083536726 95 .00268944 R-squared Adj R-squared = 0.7712 Root MSE Total | 1.25793748 107 .011756425 - .05186 ltotacc | Coef. Std. Err. t P>It| [958 Conf. Interval] .0024274 -.0912208 .031287 .0027471 .0001611 .0244475 .0244491 17.06 0.000 .0030669 .0058479 .1283621 feb | -.0426865 mar | apr | may | jun | jul | aug | sep I oct I…
Find a logistic function that satisfies the given conditions: initial value = 9, limit to growth = 27, passing through (2, 5) %3D 5 hp C