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- Suppose that a particular plot of land can sustain 500 deer and that the population of this particular species of deer can be modeled according to the logistic model as dPdt=0.2(1P500)P. Each year, a proportion of the herd deer is sold to petting zoos. a. Find the function that gives the equilibrium population for various proportions. b. Determine the maximum number of deer that should be sold to petting zoos each year. Hint: Find the maximum sustainable harvestTable 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?
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?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.Given the logistic growth model: N(t) = k / 1 + be^-rt Which statement below is false? a) Initially, the graph resembles an exponential function. b) The t-value of the inflection point is the time of the most rapid growth. c) The constant b in the formula above can be found using the equation: b = ( k / N (0) ) − 1. d) The function value at the inflection point is half of the carrying capacity. e) The graph is concave down before the inflection point, and concave up after the inflection point. f) After the inflection point, the growth rate declines to a limiting value.
- Show that solving the logistic differential equation results in the logistic growth functionHow is the slope coefficient interpreted in a log-linear model, where thedependent variable is (i) in logarithms but the independent variable is not, (ii)in a linear-log model, (iii) in a log-log model?Coronavirus disease (COVID-19) is spreading in a small country with a population of 100,000 people. Assume that the virus follows the Logistic Model for population growth. If 1,000 people were infected initially and 4000 were infected after 7 days, how long it will take for half the population to be infected?
- 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.A curve representing the total number of people, P, infected with a virus often has the shape of a logistic curve of the form L 1+ Ce-kt with time t in weeks. Suppose that 10 people originally have the virus and that in the early stages the number of people infected is increasing approximately exponentially, with a continuous growth rate of 1.78. It is estimated that, in the long-run, approximately 5000 people will become infected. P = (a) What should we use for the parameters k and L? NOTE: Enter the exact answers. k L = (b) Use the fact that when t = 0, we have P = 10, to find C. NOTE: Enter the exact answer. CThe logistic growth function Pok Po+(K-Po)e-rot P(t) is used to model population growth, where Po is the initial population at time t = 0, K is the carrying capacity, and ro is the base growth rate. The carrying capacity is a theoretical upper bound on the total population that the surrounding environment can support. The logistic model can be used for situations in which the initial population Po is above the carrying capacity K. Consider a deer population of 1500 on an island where a fire has reduced the carrying capacity to 1000 deer. Assuming a base growth rate of ro = 0.1, how fast (in deer per year) is the population declining when the population reaches 90% of the initial population? (Type the final answer to the nearest integer)