1.) (Sections 4.1 & 4.2) A virus is spreading through a population, with 8% more people actively infectedevery 10 days. Initially there were 102 people actively infected.(a) Find an exponential model of the form V(t) = Ab' that will compute the number of people activelyinfected V as a function of t in days.(b) What is the per-day rate of infection? Give as a percentage accurate to two decimal places (1.23%per day, for example).(c) What is the doubling time for infections? That is, how long until twice as many people are infectedthan initially? Give accurate to the nearest integer and label appropriately.

Answered: 1.) (Sections 4.1 & 4.2) A virus is…

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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22
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?
The table shows the age-adjusted death rates per 100,000 citizens for heart disease in a certain country. Complete parts (a) and (b) below. (a) Find an exponential model of the form f(t)=yob' for these data, where t=0 corresponds to the year 2000.Use the first and last data points to find a function. 1(t)=¹ (Round to two decimal places as needed.) (b) Assuming the model remains accurate, estimate the death rate in 2019 and 2024. The death rate in 2019 will be (Round to one decimal place as needed.) people per 100,000 The death rate in 2024 will be (Round to one decimal place as needed.) people per 100,000. Year 2000 2002 2004 2006 2008 2010 2012 2014 Death Rate 257.4 239.4 215.0 211.9 185.6 178.9 171.8 166.0
Question 8 Find the average rate of change of g(x) = - 2x- 2 between the points (-2,-10) and (4,-34) > Next Question
A scientist is studying three different cultures of bacteria {labeled "A", "B" and "C"} and wants to mathematically model the bacterial change of each type. To do this, the scientist decides to collect data for 25 consecutive days and builds the following scatter diagrams where the horizontal axis corresponds to "t" and the vertical axis to the amount of bacteria present in the culture P = P (t) Help the scientist decide which mathematical model (initial value problem) to use for each of the three types of crops. To do this, associate each of the graphs above with one of the following initial value problems. Crop type A a) dP/dt = k with P(0)=P0 and k>0.b) dP/dt = k with P(0)=P0 and k<0.c) dP/dt = kt with P(0)=P0 and k>0.d) dP/dt = kt with P(0)=P0 and k<0.e) dP/dt = kP with P(0)=P0 and k>0.f) dP/dt = kP with P(0)=P0 and k<0.g) dP/dt = kP(1-P/M) with P(0)=P0 and M, k>0.h) dP/dt = kP(1-P/M) with P(0)=P0 and M, k<0. Crop type B a) dP/dt = k with P(0)=P0 and…
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10.23. Question. An umbrella-shaped island has a population of 499 healthy people. Alice, who is injected with the T-virus, enters the island on day 0. It is known that anyone infected with the T-virus will become a zombie after 24 hours. Assume that the infected (zombies are considered infected) will spread the virus (through biting) and no one on this island can escape from it. The rate of virus transmission 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, then dx dt = 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 boat should be sent to ensure it can rescue all survivors (those not infected)?
5. The lifetime of a piece of equipment L follows an exponential distribution with mean 1 year. The tax depreciation factor D for writing off the cost of replacing the component after it fails is D = e-L where L is the age of the component in years when it fails and needs to be replaced. The taxable value T of the piece of equipment over its lifetime is then T = v(1 – D) where v is the initial value (cost) of the piece of equipment. What is the expected taxable value over its lifetime of a piece of equipment that initially cost $1000?
Q1. Assume that the rate at which radioactive nuclei decay is proportional to the number of such nuclei that are present in a given sample. In certain sample 10% of the original number of radioactive nuclei have undergone disintegration in a period of 100 years. a) What percentage of the original radioactive nuclei will remain after 1000 years? b) In how many years will only one-fourth (1/4) of the original number remain?
2. Below are three exponential equations. Create a situation/context that could model each of the equations. a) y = 450('/2)* b) N(t) = 7100(3) () c) 75 = 4
7 In a G/G/3 system with average service time equal to 6.9 minutes, average time in system equal to 25.1 minutes, what is the average wait in queue?

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