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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The following data show the number of people (in thousands) who own a DVD player in a large city or linear is best for over a period of years. 1999 2001 Year Number of DVD Owners (thousands) 1998 23 27 2000 31 37 2002 43 a) Use your model to predict how many people will own a DVD player in the year 2015. b) Predict the instantaneous rate of change in the number of DVD players in this city in 2000.
What does February 2020’s actual grocery store sales value tell us about the strength of this model to extend past the ten years covered in the scatterplot?
The following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2032. 2012 2014 2016 2018 2020 CO2 Emissions 338.5 364.5 397.1 423.8 452.1 498.4 Year 2010 Year 2022 2024 2026 2028 2030 CO2 Emissions 557.2 592.9 628.7 662.1 707.1 (a) Create a linear function that models these data, with x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions. (Round all numerical values to two decimal places.) y(x) = 2032 741.7 (b) Find the model's estimate for the 2024 data point. (Round your answer to two decimal places.) million metric tons Interpret the slope of the linear model. For each year since ---Select--- (c) Find the slope of the linear model. (Round your answer to two decimal places.) , carbon dioxide emissions in the U.S. are expected to change by million metric tons.
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?
Derive the least squares estimators (LSEs) of the parameters in the simple linear regression model.
Consider a two component parallel system in which both components have times to failure and times to 0.0024 f/hr and µ1 = = 0.001 f /hr, 12 repair that are exponentially distributed. The data is 1, 0.003 r/hr and µ2 = 0.005 r/hr. Evaluate the reliability or probability of success for a mission of 1000 hr. (hint: form a history for each component using the data for failure rate and repair rate)
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Is the following statement true or false? If false explain briefly. Some of the residuals from a least squares linear model will be positive and some will be negative. (Don't Hand writing in solution)
cipate worth S Exercise 2.9.8. [S][Section 2.1][Goal 2.1][Goal 2.5] Counting red blood cells. On page 240 of the April 2011 issue of the Bulletin of the American Mathematical Society Misha Gromov wrote that Erythrocytes are continuously produced in the red bone marrow of large bones... at the rate ~ 2.5 million/second or~ 200 billion/day. Adult humans have 20-30 trillion erythrocytes,~ 5 million/ cubic millimeter of blood. [R54] (a) What is an erythrocyte? (b) Check that 2.5 million/second is about 200 billion/day. (c) Use the numbers in the second sentence to estimate the volume of blood in an adult human, in liters. (d) Check your answer to the previous question with a web search.
What does February 2020’s actual warehouse club sales value tell us about the strength of this model to extend past the ten years covered in the scatterplot?
Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain
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…

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