B. Fill in the blanksYou have 1000 bugs in a bottle. It is known that the bug population is given by the logistic model with a birth rate per capita of 20% per week. After avery iong time, you found that the bug population had attained an equilibrium value of 5000. You then started an experiment with an antibiotic whichKilied E bugs per week, where E is a positive integer. After another very long time, you found that the bug population had attained anotherequilibrium value of 3000. Then the value of the positive integer E is 1 .Enter the correct answer below.Flease enter a number for this text box

Answered: Image /qna-images/answer/4ed0061c-e87b-4c0b-baf8-aadd75a01f37.jpg

Answered: You have 1000 bugs in a bottle. It is…

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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Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1200 fish. Absent constraints, the population would grow by 110% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
Biologists release two otters (a type of water animal) into a river. They believe that the river could support a maximum population of 500 otters, and that with unlimited resources the otter population would increase by 50% each year. i. Write down a Pielou logistic equation to model the yearly otter population, of the form Yn+1 Xyn 1+ Byn for suitable a, ẞER. ii. By solving this equation, make a prediction of the population after 5 years.
In the early 1980s, AIDS (Acquired Immune Deficiency Syndrome) spread rapidly. A logistic curve modeling the spread of the disease in the United States is given by 47500 P(t) = 1+ 148.41e-0.8t where t is measured in years since 1981 and P is the number of reported cases. In what year does this model predict that the number of new cases will be growing at the largest rate? Remember to fully justify your answer.
Consider two populations that can be modeled by the logistic equation with the same carrying capacity, but with different values of k. Which population approaches the carrying capacity most quickly, the one with the smaller or larger value of k? You may want to think geometrically (check out some slope fields), analytically (look at the form of the solution), or num into the solution). erically (plug some t values
Consider a lake that is stocked with walleye pike and that the population of pike is governed by the logistic equation (check the image) where time is measure in days and P in thousands of fish. For part a I assumed that I needed to subtract 10 from everything, and then I drew my phase line (part b). my answers for this didnt make a lot of sense and I think that I did it wrong. Part D is the same as a and I think that I subtract .02P from everything. can you please go over this to make sure that it works?
A new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960.
Suppose that you decide to fit a logistic regression model using these data. Let Y = 1 if a subject develops cancer and 0 otherwise. Let Finasteride = 1 if a subject received Finasteride and 0 if they received placebo. The estimated logistic model is What is the value of ?
in 2017, the residents of eugene were producing greenhouse gas emissions at an average rate of 16 tons of co2 per resident per year, and that the amount was decreasing at an instantaneous rate of .22 tons per year. however the population of euegene was 170,000 and growing at a rate of 2,000 people per year. at what instantaneous rate was the total greenhouse gas emissions in eugene growing in 2017 ?
Suppose the population of a species of animals on an island is governed by the logistic model with relative rate of growth k = 0.05 and carrying capacity M= 15000. I.e., the population function P(t) satisfies the equation P' = bP(15000 - P), where b = k/M. If the current population is P(0) = 20000, which one of the following is closest to P(1)? O a) 19700 O b) 19890 Oc) 19680 Od) 19690 Oe) 19805 Of) 19742 Motion
I have tried 8 percent, 0.080, 0.079, and many others however I am still stuck on this problem. I even tried a different method that gave me 11.82 still wrong.
A study of Maryland's portion of Chesapeake Bay found the following information about stocks of market-sized oysters.† In 1994, the stocks were 218 million. (This is the number you will use for the initial population N(0).) The carrying capacity is 5089 million oysters. The intrinsic exponential growth rate is 0.274 per year. (a) Find a logistic model N(t) for the number, in millions, of market-sized oysters. Take t to be the time in years since 1994. (Rround all regression parameters to three decimal places.) N(t) = (b) Plot the graph of the model you found in part (a) over the first 20 years. (c) How many market-sized oysters does your model predict for 2007? Round your answer, in millions, to the nearest whole number. million oysters (d) The actual number of market-sized oysters was found to be 82 million. Use the Internet to find possible explanations for the reduced levels of oysters in Chesapeake Bay.
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=300, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =

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