A biologist is tracking Lyme Disease cases in a deerpopulation of 8500 in a state forest in Wisconsin.Suppose at time t = 0 the number D(t) of deer withLyme Disease is 2250 and is increasing at a rate of 110deer per month. Assume that D'(t) is proportional tothe product of the number of deer who have caughtLyme's disease and of those who have not.(a) Write a differential equation to represent thisscenario. Use k for your proportionality constant andD(t) as your function (not D).D'(t)=(b) If you did part (a) correctly, the general solution.to your differential equation isD(t)=85001+Ce-8500ktFind C (keep C exact).C=(c) Find k. (Hint: you do NOT need the function inpart (b) to find k). Keep k exact.k(d) How long will it take for 50% of the deerpopulation to develop Lyme Disease? Keep k and Cexact until your final calculation. Round your finalanswer to two decimal places.months

c) Finding k110 = k * 2250 * (8500 - 2250)k = 110 / (2250 * 6250) k = 1/125000 d) Time for 50%…

Answered: A biologist is tracking Lyme Disease…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
What is the y -intercept on the graph of the logistic model given in the previous exercise?
In 2007, (when t = 0), world solar photovoltaic (PV) market installations were 2826 megawatts and were growing exponentially at a continuous rate of 48% per year. Write a differential equation to describe the relationship in the form of dS/dt.
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The rate of growth of a population of a city is given by: P' = 2000t1.04 where P is the population and t is the number of years past 2015. If the population in the year 2015 is 50,000, what is the predicted population in the year 2025? O 107,498 5.45 Billion O 746,943 O 157,498
Annual U.S. imports from a certain country in the years 1996 through 2003 can be approximated by I(t) + 3.6t+47 (1st s9) billion dollars, where t represents time in years since 1995. Annual U.S. exports to this country in the same years can be approximated by E(t) 0.5²-1.4t+16 (0 sts 10) billion dollars. Assuming the trends shown in the above models continue indefinitely, numerically estimate the following. (If an answer does not exist, enter DNE.) im E(t) and lim 7-*** lim e(t)- E(t) lim 1-+= 1(1) - E(E) (1)
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Before current environmental regulations were in place, a certain manufacturing plant released pollutants into a stream that feeds into a small lake. The pollutants in the lake water have been deteriorating over time and are currently changing at a rate that can be modeled by the function P'(t)=1–3e02di , in gallons/year. A local college professor has been taking her classes to monitor the pollutant levels for the past 5 years. They estimated the pollutant levels to be 50 gallons their first year of collecting data (time t = 0). A level of <38 gallons is considered safe. a. Show that the pollutants in the lake are currently decreasing (t= 5). b. Use methods of calculus to determine the value of t for which the pollutant levels are at a minimum. c. Use methods of calculus to determine whether the pollutant levels are considered safe at the time you found in part (b).
Americium-241 is a radioactive isotope commonly found in ionization-type smoke detectors and has a half-life of 432 years. From a 75-gram sample of americium-241, which equation models the amount remaining after t years? 'A (t) = 75(금) 표 A (1) = 432(1) ㅎ 'A (1) = 75(1) 푸 A (t) = 432(})#

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