help with b and c. NO AI (Sec 11.1) Consider the spreading of a highly communicable disease on an iso-lated island with population N. A portion of the population travels abroad andreturns to the island infected with the disease. You would like to predict thenumber of people X who will have been infected by some time t. Consider thefollowing model, where k > 0 is constant:dXdt=kX(N-X)(a) List two major assumptions implicit in the preceding model. How reason-able are your assumptions?(c) Graph X versus t if the initial number of infections is X₁ < N/2. GraphX versus t if the initial number of infections is X2 > N/2.(d) Solve the model given earlier for X as a function of t.(e) From part (d), find the limit of X as t approaches infinity.

Part b Part cFor part (c), solving the differential equation:This solution provides X as a…

Answered: (Sec 11.1) Consider the spreading of a…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 33EQ

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.
A model is built to explain the evolution of spending on tourism and recreation in a certain group of families (Y in USD/person/year). As potential explanatory variables are considered: X1 average annual income per person in the family (in USD), X2 – number of people in the family, X3 – nature of employment of the head of household If X3=1, when the head of the family is self-employed, X3=0, when the head of the family is an employee Based on the collected data, linear correlation coefficients between variables were calculated and obtained 0,84 R, = -0,47 [1 -0,55 0, 62 R= 1 -0,42 0,75 1 Using Hellwig's method, select the optimal combination of explanatory variables for the tourism and recreation expenditure model.
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.
An ecologist is studying the impacts of air pollution on giant panda populations, specifically on panda birth rates. Due to the historical interest in giant pandas, the ecologist has access to data from the last 30 years that allows her to fit two models to the evolution of giant panda populations over time (one for 30 years and one for the last 5 years after a new chemical plant was built close to the panda habitat). She will use these models to determine the long-term impacts of this pollution on panda populations. She has the following information to help her model the two sets of population dynamics data on adult and baby pandas : i. 1) Without pollution, for every 1 adult female panda a year earlier, 0.75 baby pandas are born each year (reproduction rate = 0.75). 2) With pollution, for every 1 adult female panda a year earlier, 0.7 baby pandas are born each year (reproduction rate = 0.7). 3) 3 in 4 of the adult female pandas survive to the next year. 1 in 3 female baby pandas…
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Find the linearization at x = a. 1 f(x) = = 5 +3
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The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.0250.025 level of significance. Swimmers at the City Pool Monday Tuesday Wednesday Thursday Friday Number 4141 6868 6464 5757 6969 Copy Data Step 1 of 4: State the null and alternative hypotheses in terms of the expected proportion for each day. Enter your answer as a fraction or a decimal rounded to six decimal places, if necessary. H0: pi=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ Step 2 of 4: Calculate the expected value for the number of swimmers on Tuesday. Enter your answer as a fraction or a decimal rounded to three decimal places. Step 3 of 4: Compute the value of the…
b) Data was collected on 344 corporate executives to find out the effect of MBA degree and work experience on their salary. The following model was estimated: Y; = 2.3501 + 3.6306D, – 2.6354 D2i + 0.8527 X; + 1.634 (D, * X); t = (1.263) (2.1805) (- 3.457) (7.605) (2.98) R? = 0.8968 Y: Annual Income in Lakhs of Rupees Di and D2 are MBA and gender dummies respectively X: Work experience in years DI = 1 if one has MBA degree = 0 otherwise D2 = 1 for a female executive = 0 for a male executive i. Write the regression equations for female MBA executives and male MBA executives separately. ii. Find the mean income level for the reference category and interpret it. iii. Test the statistical significance of differential intercept coefficient between female MBA executives and Male MBA executives at 5% level of significance. iv. Interpret the coefficient of Di*Xi. v. Now suppose out of this sample of 344 executives, 48 are female MBA executives and 156 are male MBA executives. To find out the…
6. 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 = kP 3 (a) Use the differential equation to show that any solution is incaeasing if m < P < M and decreasing if 0 < P < m. (b) For the case where k = 1, M = 100, 000 and m = 10,000, draw a direction field and use it to sketch several solutions for various initial populations. What are the equilibrium solutions? (c) One can show that M(P, – m)em - m(Po – M) P(t) M-m) (Po – m)e (Po – M) is a solution with initial population P(0) = Po. Use this to show that, if P(0)
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