(c) The mean and variance of X. Mean = i (Round your answer to 2 decimal places.) Variance = i (Round your answer to the nearest integer.)
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- Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.What is the y -intercept on the graph of the logistic model given in the previous exercise?Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?
- Use log21=0,log22=1, and log24=2 to estimate log23.An individual improperly disposes of 8 parakeets in a nearby woodland, where they begin to reproduce at an initial rate of 3 parakeets per month. Write a differential equation for the population P assuming logistic growth, where the woodland can support at most 500 parakeets. (Do not round any coefficients.) dP/dt =The total number of reported cases of an illness in a large city days after the start of an outbreak is modeled by the function y = F(t) that is a solution to the logistic differential equation dy/dt= (1/5600)y(1400-y). If there are 5 reported cases of the illness initially, what is the limiting value for the total number of reported cases of the illness as t increases?
- Write a logistic differential equation that models the growth rate of the brook trout populationin Item (1). Then repeat part (b) using Euler's Method with a step size of h = 1. Compare theapproximation with the exact answer.Verify by substitution that each given function is a solution of the given differential equation. Primes denote derivatives with respect to x.Has to be compounded continuously
- Suppose a population grows according to a logistic differential equation model. Its population in 2000 is 500 and carrying capacity is 10,000. If the population is 1,500 in 2001, what will the population be in 2002?Find the logistic differential equationThe logistic model can also be changed by incorporating a constant continuous rate of decrease, such as due to hunting: dP/dt=kP(1-P/A)-H where H members of the population are removed per year (over the course of the year). Suppose a population of fish obeys the logistic differential equation with k = 0.08 and carrying capacity A = 1000. (a) Suppose c = 15 fish are caught by fishers per year. Draw a slope field for the resulting differential equation, and identify the equilibrium solutions (where y′ = 0). (b) Suppose instead c = 25 fish are removed each year. Draw the resulting slope field. What effect does this have on the fish population overall? (c) Find the maximum annual amount of hunting c > 0 that allows the population of fish to survive. Graph the slope field for this differential equation. (d) If you worked for the forest service, make a recommendation for how much fishing to allow per year to ensure sustainable fishing.