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- Suppose that the DE dy/dt = y(70 - y ) - 600 models a logistic equation with harvesting, where y(t) represents a tilapia population in a lake at time t, measured in years.you have to responsibility to manage a 100 heactaere forest with a matur stock of 800 cubik meters per hectare having mean annual increment of 10 cubis meter per hectare per year ,over a planed rotation of 20 year . an application of area control will lead to an annual harvest of (a) 5000m3/year (b) 5ha/year (c) 4000m3 (d) 15ha/yearThe time to first failure X of the software of a medical linear acceleratormay be modeled normal with μ = 1100 hours and σ = 50 hours.
- Find the linearization of ƒ(x) = log3 x at x = 3. Then round its coefficients to two decimal places.After constant complaints about the long wait from his customers, Ryan - the owner of shop - hasdecided to hire a second mechanic to handle installations. Customers, who arrive at a rate ofabout 3 per hour (Poisson), will wait in a single line until one of the two mechanics is free. Eachmechanic can serve about four customers per hour (Exponential).Do you think the improvement on customer experience will be significant? Computethe key waiting line characteristics BEFORE and AFTER the second mechanic is hired tosupport your answer.Suppose that a healthy population of some species is growing in a limited environment and that the current population P0 is fairly close to the carrying capacity M0. You might imagine a population of fish living in a freshwater lake in a wilderness area. Suddenly a catastrophe such as the Mount St. Helens volcanic eruption contaminates the lake and destroys a significant part of the food and oxygen on which the fish depend. The result is a new environment with a carrying capacity M1 considerably less than M0 and, in fact, less than the current population P0. Starting at some time before the catastrophe, sketch a “before-and-after” curve that shows how the fish population responds to the change in environment.
- Give the family of orthogonal trajectories for the equation: y2 = Cx5+5Suppose that the growth-rate parameter k = 0.3 and the carrying capacity N = 2500in the logistic population model of Exercise 17. Suppose P(0) = 2500.(a) If 100 fish are harvested each year, what does the model predict for the longtermbehavior of the fish population? In other words, what does a qualitativeanalysis of the model yield?(b) If one-third of the fish are harvested each year, what does the model predict forthe long-term behavior of the fish population?In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.97x2.1 for one year to y = 0.35x2 + 0.65x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) before after
- Give the family of orthogonal trajectories of y^2=Cx^5+5.Women in the Workforce The following table givesthe number of women age 16 years and older (inmillions) in the U.S. civilian workforce for selectedyears from 1950 and projected to 2050.a. Use x as the number of years past 1950 to create acubic model using these data.b. During what year does the model indicate that thenumber of women in the workforce will reach itsmaximum?A recent report by the U.S. Cen- sus Bureau predicts that the U.S. Hispanic population will increase from 35.6 million in 2000 to 102.6 million in 2050. Assuming the unlimited growth model dy/dt = ky fits this population growth, express the population y as a function of the year t. Let 2000 correspond to t = 0.