Concept explainers
Applications
44. Logistic equation for spread of rumors Sociologists model the spread of rumors using logistic equations. The key assumption is that at any given time, a fraction y of the population, where 0 ≤ y ≤ 1. knows the rumor, while the remaining fraction 1 – y does not. Furthermore, the rumor spreads by interactions between those who know the rumor and those who do not. The number of such interactions is proportional to y(1 – y). Therefore, the equation that describes the spread of the rumor is y′(t) = ky(1 – y), where k is a positive real number. The number of people who initially know the rumor is y(0) = y0, where 0 ≤ y0 = 0.1
- a. Solve this initial value problem and give the solution in terms of k and y0.
- b. Assume k = 0.3 weeks–1 and graph the solution for y0 = 0.1 and y0 = 0.7.
- c. Describe and interpret the long-term behavior of the rumor function, for any 0 ≤ y0 ≤ 1.
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Chapter D1 Solutions
CODE/CALC ET 3-HOLE
Additional Engineering Textbook Solutions
Glencoe Math Accelerated, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
University Calculus: Early Transcendentals (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- Modeling and Simulation Q) The number of hurricanes hitting the coast of Florida annually has a Poisson distribution with a mean of 0.7. What is the probability that more than one hurricanes will hit the Florida coast in a year ?arrow_forwardInformation on morphine: Morphine can be administered via injection / IV. The quantity of morphine in a given dose may vary, but one guideline is to use 0.1 mg of morphine for each kg of the patient's body mass. The time taken for half the quantity of morphine to be removed from the body is 2 hours. An exponential function can be used to model the amount of morphine in the body over time: ?=?0???A=A0ekt (note that ?k will be negative). Calculate the value of ?k for morphine. Write a Python function called MorphineModel, which takes two arguments: dose amount ?0A0 and time since last dose ?t, and returns the amount of morphine in the body at this time ?t. Add to your computer code so that you have a program which is an implementation of the following flowchart. Ensure that your code is well-communicated to a user of the program (via the print statements) and well-communicated to someone reading the code (via comments).arrow_forwardSolve in R programming language: Suppose that the number of years that a used car will run before a major breakdown is exponentially distributed with an average of 0.25 major breakdowns per year. (a) If you buy a used car today, what is the probability that it will not have experienced a major breakdown after 4 years. (b) How long must a used car run before a major breakdown if it is in the top 25% of used cars with respect to breakdown time.arrow_forward
- TOPIC: MARKOV CHAINS A book club has 3 mailing lists: A special list M of the most senior active members. Another list R containing the regular members, and A list of regular members and names of individuals who have shown interest in club activities in the past. For each new publication, it is necessary to decide which list should be used to mail the sale announcements.sale.If after the last mailing there was a request for too few copies, the secretary uses list R with probabilityof ¼ and P with a probability of ¾.If after the last mailing there was a satisfactory response, the secretary uses the R list and the P list with equalprobabilities.If, after the preceding shipment, there was an excessive number of orders or over demand, the secretary uses list M with probability 1/3 and list P with probability ¾.list M with probability 1/3 and R with probability 2/3.If list M is used, there will be poor sales or satisfactory sales with equal probabilities; if list R is used, there will be…arrow_forwardUnder all..arrow_forwardSuppose that the grading of x University courses is as follows:• Each student can get grades between 0 and 100.• If the student's grade is less than 40, the student is informed that the course failed (Unsuccessful).• If the student's grade is higher than 40,o The difference between the student's current grade and the number that is a multiple of 5 higher than the closest to his / her grade is less than 3.If it is lower, the student's grade is equal to the 5 fold higher than the closest one.o If the difference is 3 or more than 3, no change is made in the grade of the student.In this context, the updated grades of the students are calculated according to the entered student gradesWrite the Java code showing.Solve this question in c ++ language.ü Define the section to be calculated as Java object ("Question1").ü Question1; Take the note string as input.public Question1 (int [] input)ü Print out the updated notes as a series after the calculation is madeo public int [] gradingStudents…arrow_forward
- Suppose that the grading of x University courses is as follows:• Each student can get grades between 0 and 100.• If the student's grade is less than 40, the student is informed that the course failed (Unsuccessful).• If the student's grade is higher than 40,o The difference between the student's current grade and the number that is a multiple of 5 higher than the closest to his / her grade is less than 3.If it is lower, the student's grade is equal to the 5 fold higher than the closest one.o If the difference is 3 or more than 3, no change is made in the grade of the student.In this context, the updated grades of the students are calculated according to the entered student gradesWrite the Java code showing.ü Define the section to be calculated as Java object ("Question1").ü Question1; Take the note string as input.public Question1 (int [] input)ü Print out the updated notes as a series after the calculation is madeo public int [] gradingStudents ()Code sample:public class Question1…arrow_forwardIn a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet. Indicate the causal relationships in this system with arrows and signs. Show the causality loops in this system, at least 1 negative, at least 1 positive, and…arrow_forwardIn a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet.arrow_forward
- A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores, 9 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen? Your answer is:arrow_forwardCorrect answer will be upvoted else downvoted. Computer science. in case there are two planes and a molecule is shot with rot age 3 (towards the right), the cycle is as per the following: (here, D(x) alludes to a solitary molecule with rot age x) the primary plane delivers a D(2) to the left and lets D(3) progress forward to the right; the subsequent plane delivers a D(2) to the left and lets D(3) progress forward to the right; the primary plane lets D(2) forge ahead to the left and creates a D(1) to the right; the subsequent plane lets D(1) progress forward to one side (D(1) can't create any duplicates). Altogether, the last multiset S of particles is {D(3),D(2),D(2),D(1)}. (See notes for visual clarification of this experiment.) Gaurang can't adapt up to the intricacy of the present circumstance when the number of planes is excessively huge. Help Gaurang find the size of the multiset S, given n and k. Since the size of the multiset can be extremely huge, you…arrow_forwardA group of n tourists must cross a wide and deep river with no bridge in sight. They notice two 13-year-old boys playing in a rowboat by the shore. The boat is so tiny, however, that it can only hold two boys or one tourist. How can the tourists get across the river and leave the boys in joint possession of the boat? How many times need the boat pass from shore to shore?arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
![Text book image](https://www.bartleby.com/isbn_cover_images/9780534380588/9780534380588_smallCoverImage.gif)