Confirm that the total population in this model remains constant. Let the total population size at time t be denoted by N(t).We divide the population N(t) into four subclasses: potentialsmokers (nonsmoker) P(t), smokers S(t), smokers who tem-porarily quit smoking Q,(t), and smokers who permanentlyquit smoking Q₂ (t), such that N(t) = P(t) + S(t) + Q₂(t) +Qp(t). We describe the dynamics of smoking by the followingfour nonlinear differential equations:dpdt=H-HP-BPS,ds- (µ+ y) S + BPS + αSQ₁dtdQ₂= −µQ₁ - αSQ₁ + y(1-0) S,dtdQp== −μQp + σys.dt

As per the question we are given a population model through a system of dynamic equations relating…

Answered: Let the total population size at time t…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Researchers have created every possible "knockout" line in yeast. Each line has exactly one gene deleted and all the other genes present (Steinmetz et al. 2002). The growth rate—how fast the number of cells increases per hour—of each of these yeast lines has also been measured, expressed as a multiple of the growth rate of the wild type that has all the genes present. In other words, a growth rate greater than 11 means that a given knockout line grows faster than the wild type, whereas a growth rate less than 11 means it grows more slowly. The growth rate of a random sample of knockout lines is 0.86, 1.02, 1.02, 1.01, 1.02, 1, 0.99, 1.01, 0.91, 0.83, 1.01 What is the standard deviation and variance of growth rate for this sample?
A research study in a big metropolitan area shows that 2% of individuals living within the city limits move to suburbs during one-year period while 1% of individuals living in the suburbs move to the city during a one-year period. 1. A group of 100 individuals are now living in the city, how many of them will stay after 3 years.
Over the past 10 years (actually, 2007 to 2017), it is estimated that the population of China has increased from 1.318 billion to 1.386 billion people, whereas the population of India has increased from 1.18 to 1.339 people. If both countries continued to grow at these rates, will China or India have the greater population in 2027? Show your calculations below.
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It is known that in any given year, • 90% of the people in a city move to the suburbs; • 80% of the people in the suburbs do not move to the city. Given an initial city population of 55,000 and an initial suburb population of 77,000, what are the long-term population levels of the city and the suburb?
A bacteria culture had a population of 13 million at 10:00 am and by 2:00 pm had grown to 21 million. Predict the population at 6:00 pm that same day.
Two numbers are greater than 10 but less than 40. Their GCF is 17. What are the two numbers?
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 60 cells.
A popular social media platform has begun offering stock shares to the public. In the past 2 years, the price of the stock has generally increased. An investment specialist gathers data on the stock price over the past 2 years and proposes two models for estimating the growth of the stock, as shown in the scatterplots. Based on the scatterplots, which type of model is most suitable for estimating the stock price? O A power model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship. O A linear model is suitable because the scatterplot of weeks against log(stock price) shows a strong linear relationship. log(Stock Price) vs. Weeks 2.28 O An exponential model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship. 2.26 2.24 2.22 22 P2.18 2 16 * 214 212 21 2.08 O An exponential model is suitable because the scatterplot of weeks against log(stock price) shows a strong linear relationship. Mark…
A poultry raiser harvests an average of 300 eggs per day. He has recently experimented with different types of poultry feeds. As a result, he noticed some fluctuations in the number of eggs laid by the chickens, which is neither clearly higher nor lower than previous weeks. He decides to find out if there might be a significant change in the number of eggs laid by the chickens. He records his harvest of eggs for 20 days. He finds that the average per day is 290 eggs with a standard deviation of 15. At 5% Level of Significance, what did the poultry raiser concludes?

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