10.23. Question. An umbrella-shaped island has a population of 499 healthy people. Alice, who is injectedwith the T-virus, enters the island on day 0. It is known that anyone infected with the T-virus willbecome a zombie after 24 hours. Assume that the infected (zombies are considered infected) willspread the virus (through biting) and no one on this island can escape from it. The rate of virustransmission is proportional to the product of the number of infected and non-infected. Thus, if x(t)denotes the number of the infected on day t, thendxdt= kx(500 — x).On day 10, it is observed that 20 people are already infected. Answer the following questions.(a) How many zombies are on the island on day 16?(b) On day 20, how many people are infected but not yet turned into a zombie?(c) A rescue boat with 50 available seats is to be sent to the island. What is the earliest day the boatshould be sent to ensure it can rescue all survivors (those not infected)?

Approach to solving the question: Recognize the Type of Differential Equation: The given equation is…

Answered: 10.23. Question. An umbrella-shaped…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Chapter 11-2. The following table presents the numbers of cucumber seeds, by brand, that germinated or failed to germinate 14 days after planting. Brand A Brand B Brand C Brand D 27 Germinated 28 33 36 Failed to Germinate 5 17 4 5 Can you conclude that the the germination rate is related to the brand of seed? Use the a = 0.05 level of significance. Reject Ho. It appears that the germination rates differ among the seed brands. Do not reject Ho. There is insufficient evidence to conclude that the germination rate differs among the seed brands.
An investigator modeled the log-odds of getting stomach cancer as a function of number of servings of vegetables per week and the number of servings of red mean per week using logistic regression. The odds that a person gets stomach cancer if they have 4 servings of red meat a week are 1.2 times the odds of cancer for someone who has 3 servings of red meat a week. Suppose the fitted regression model is given as log-odds = -6 + 0.182 M – 0.105 V, where M = #servings of red meat per week and V = #servings of vegetables per week. What is the odds ratio representing the change in odds for an increase in one serving of vegetables? Give the answer to three decimal places.
4. Suppose that antibiotics are injected into a patient to treat a sinus infec- tion. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. The following is a model for the concentration (in µg/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. e-at – e-ßt C(t) В — а where a and B are constants with ß > a > 0. (a) occurs. (Your argument must use the first derivative test.) Using the first derivative test, find when the maximum concentration (b) (Your answer should be supported by a rigorous argument.) When does the rate of change of concentration begin to increase?
A scientist is interested in two different types of particles; type A and type B. The time that it takes for a particle of type A to decay can be modeled as an exponential distribution with a mean of 75 minutes, and the time that it takes for a particle of type B to decay can be modeled as an exponential distribution with a mean of 50 minutes. Suppose that a container holds 10 particles; 7 of type A and 3 of type B. Assume that the rate at which each of the particles decays is independent of all of the other particles in the container. (1) Calculate the probability that the first particle to decay is of type A. (2) Calculate the probability of the following event; "it takes at least 30 minutes for any of the particles to decay, and the first particle that decays is of type B".
Question 9?
1.2.4. Consider the spreading of a highly communicable disease on an isolated island with population size N. A portion of the population travels abroad and returns to the island infected with the disease. Formulate a dynamical system to approximate the change in the number of people in the population who have the disease.
Pesticide danger: One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which a pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the length of the contact, or whether it increases for only a short time before leveling off. To investigate this, measured amounts of a certain pesticide were applied to 20 samples of rat skin. Four skins were analyzed at each of the time intervals 1, 2, 4, 10, and 24 hours. The amounts of the chemical (in micrograms) that were in the skin are given in the following table.
19.
One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which a pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the length of the contact, or whether it increases for only a short time before leveling off. To investigate this, measured amounts of a certain pesticide were applied to 20 samples of rat skin. Four skins were analyzed at each of the time intervals 1 , 2 , 4 , 10 , and 24 hours. The amounts of the chemical (in micrograms) that were in the skin are given in the following table. Duration Amounts Absorbed 1 1.8 1.9 1.8 2.2 2 1.5 2.4 1.5 2.5 4 1.5 2.7 1.3 1.9 10 1.3 1.5 1.4 2.6 24 1.8 1.3 2.3 1.8 Construct an ANOVA table. Round your answers to four decimal places. One-way ANOVA: Pesticide Amount…
3. The following model is estimated: sleep = 3840.83 - 0.163totwrk + 11.71educ + 8.70age +0.128age? + 87.75male, I (235.11) (0.018) (5.86) (11.21) (0.134) (34.33) n = 706, R = 0.123 The variable sleep is total minutes per week spent sleeping at night, totwrk is total weekly minutes spent working, educ and age are measured in years, and male is a gender dummy. (a) All other factors being equal, is there evidence that men sleep more than women? Test the null hypothesis that men sleep the same amount of time as women against the alternative hypothesis that men sleep more than women at 5% significance level. (b) Is there a statistically significant tradeoff between working and sleeping? What is the estimated tradeoff?
.A new, miracle diabetes drug that diminishes major symptoms of diabetes has been approved by the FDA. Health care professionals and researchers believe that the new drug will prolong lifespan of diabetes patients. If the population is in steady state and the incidence is constant, what will the effect of this new drug be on the prevalence of diabetes in the population? Explain.
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?

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