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- The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012, therewere 23,900 fox counted in the area. What is the foxpopulation predicted to be in the year 2020 ?Continued This is a continuation of Exercise 13. As we saw earlier, the stock turnover rate of an item is the number of times that the average inventory of the item needs to be replaced as a result of sales in a given time period. Suppose that a hardware store sells 80 shovels each year. a. Suppose that the hardware store maintains an average inventory of 5 shovels. What is the annual stock turnover rate for the shovels? How is this related to the yearly number of orders to the wholesaler needed to restock inventory? b. What would he the annual stock turnover rate if the store maintained an average inventory of 20 shovels? c. Write a formula expressing the annual stock turnover rate as a function of the average inventory of shovels, identify the function and the variable, and state the units.Acertain virus swept through a town of 1000 people. The virus caused illness that lasted an average of four days. The outbreak lasted for 12 days, reaching a peak of 200 infected people on day 5. Initially everyone was susceptible; at the end, 600 people had been infected, so 400 people were still susceptible. Assuming the SIR model applies, estimate R0 for this outbreak.
- The rate of increase of COVID-19 infection is directly proportional to the number of people infected and to the number people not yet infected. An isolated remote barangay of population 10,000 records its first case on June 15, 2020. After two days, 100 people are infected. Develop a model that predicts the number of COVID-19 cases in the barangay. How long will it take for 90% of the population to be infected? Assume that the virus persists in the person infected.Due to a stocking error 50 carp are added to a lake. The carp are prolific breeders with a population growth rate coefficient of 0.5 per month. Lake managers catch and remove K carp per month. What is the minimum number of carp that must be captured and removed to ensure they are eventually eradicated?Insulation workers who were exposed to asbestos and employed before 1960 experienced an increased likelihood of lung cancer. If a group of insulation workers has a cumulative total of 100,000 years of work experience with their first date of employment t years ago, then the number of lung cancer cases occurring within the group can be modeled using the functionN(t) = 0.00437t3.2.Find the rate of growth of the number of workers with lung cancer in a group as described by the following first dates of employment. Source: Observation and Inference: An Introduction to the Methods of Epidemiology.(a) 5 years ago(b) 10 years ago
- Alcohol-Related Traffic Accidents As a consequence of increasingly rigid rules aimed at decreasing the number of alcohol-related traffic accidents in a particular state, initial data shows that the number of such accidents has changed at a rate of R(t) = -18 - te0.2t accidents/month t months after the rules took effect. There were 2040 alcohol-related accidents for the year prior to the rules' implementation. Choose how many alcohol-related accidents were anticipated in the first year the rules were in effect.The temperature of Earth's surface is strongly influenced by the amount of carbon in the atmosphere. Each year, human activity adds another 9 gigatons of carbon to the atmosphere. 2 gigatons of this carbon is absorbed by the oceans, and 3 gigatons of this carbon is absorbed by plant growth (photosynthesis). There is currently 900 gigatons of carbon in the atmosphere. Assume that these are the only flows of carbon into/out of the atmosphere, and that the given rates stay constant over time. Write down a differential equation for the total amount of carbon in the atmosphere over time. Solve the equation and use the solution to predict how much carbon there will be in the atmosphere in 25 years.Life Span On the basis of data and projections for theyears 1910 through 2020 the expected life span ofpeople in the United States can be described by thefunction f (x) = 11.027 + 14.304 ln x years, wherex is the number of years from 1900 to the person’sbirth year.a. What does this model estimate the life span to befor people born in 1925? In 2007? (Give eachanswer to the nearest year.)b. Explain why these numbers are so different.
- The number of new domestic wind turbine generators installed each year in a particular country has been forecast to increase at a constant multiplicative rate of 15% per annum for the foreseeable future. This year (t = 0) 100 new generators were installed. What is the total number of new generators including this year's, that would have been installed within the next ten years (that is up to and including year t = 9)? Use a discrete model for the growth process.World Production of Coal A study proposed in 1980 by researchers from the major producers and consumers of the world's coal concluded that coal could and must play an important role in fueling global economic growth over the next 20 years. Suppose that the world production of coal in 1980 was 5.5 billion metric tons. If output increased at the rate of 5.5e0.05t billion metric tons/year in year t (t = 0 corresponding to 1980), determine how much more coal was produced worldwide between 1980 and the end of the twentieth century. (Round your answer to one decimal place.)Please do not give solution in image format thanku For a certian group, aggregated claims are uniformly distributed over (0, 10). Insurer A proposes stop-loss coverage with a deductible of 6 for a premium equal to the expected stop-loss claims. Insurer B proposes group coverage with a premium of 7 and a dividend (a premium refund) equal to the excess, if any, of 7k over claims. Calculate k such that the expected cost to the group is equal under both proposals.