Compute the derivative ficts of the logistic sigmoid 1 foo. 1 + exp(-x)
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- Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?What is the y -intercept on the graph of the logistic model given in the previous exercise?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 harvest
- Table 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 does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?The logistic model P(t)=96.79391/(1+0.0456e^0.1881t) represents the percentage of households that do not own a personal computer t years since 1985. a) Evaluate and interpret P(0). Evaluate P(0). b) What percentage of households did not own a personal computer in 1998? b) In what year will the percentage of households that do not own a personal computer reach 15%?
- A hunting club stocks a wildlife preserve with 20 elk. The carrying capacity of the preserve is 300 animals and the growth of the herd, allowing for the effect of controlled hunting of the elk, is expected to be modeled by the logistic curve *PICTURE* where t is measured in years. After how many years will the population be 253? Round to the nearest year.Q1) For the given function, explain the effects y=log_(2)(x+5)-6Find a formula for the exponential function of the form A=f(t)=IB^tpassing through the points (2.5, 17) and (7.4, 4)A = f(t) =?
- Find the average rate of change of g(x)=8x4+3x2g(x)=8x4+3x2 on the interval [-1,3] 2, mobile app's total income account (acct. #36p8734) in Phoenix started with a balance of 125,000 value in the year 2001. The balance increased to 170,000 value by the year 2014. Assume growth is exponential in this particular context, not linear. i) What was the annual growth rate between 2001 and 2014? Express your answers in both decimal and percentage forms. Keep at least 4 decimal places in the rate and then use that to convert to a percentage. Round your percentage to two decimal places. ii) Assume that the balance continues to grow by the same percentage. What is/was the balance in the year 2017 ? Show the equations you use, define your variables, and show all algebraic steps for full credit. Round to the nearest thousand value. Write your answer in complete sentence form.Q3 a) A researcher wants to find out what are the factors which determine the number of installs (I) of an application (app) from a famous app store. Size in Mbs (S), Reviews in *000s (Re), Ratings (0 to 5) (Ra), Price in 'Rs (P). She ran the following regressions: log I = 1.329 + 0.2356 S+0.4320 log(Ra) – 0.2678 P + 1.928 log(Re) Se = (0.63) R? = 0.734 (0.242) (1.29) (0.001) (0.156) df = 156 i. Interpret the regression above. ii. Test for statistical significance of Price in the model. Depending on the result do you suggest that price is a significant factor affecting app installation? iii. Suppose the regression is re-estimated where number of installs (I) varies only with respect to price (P). Average I in sample is 5 and average P is Rs 8.9. Following regression was estimated: I = 52.351 + 3.139 - se = (37.39) (0.0187) df = 156, R? = 0.806 How would you interpret this model? Explain the shape of the curve. iv. What would be the slope and elasticity of number of installs with…Q3 a) A researcher wants to find out what are the factors which determine the number of installs (I) of an application (app) from a famous app store. Size in Mbs (S), Reviews in *000s (Re), Ratings (0 to 5) (Ra), Price in 'Rs (P). She ran the following regressions: log I = 1.329 + 0.2356 S+0.4320 log(Ra) – 0.2678 P + 1.928 log(Re) Se = (0.63) R? = 0.734 (0.242) (1.29) (0.001) (0.156) df = 156 i. Interpret the regression above. ii. Test for statistical significance of Price in the model. Depending on the result do you suggest that price is a significant factor affecting app installation? iii. Suppose the regression is re-estimated where number of installs (I) varies only with respect to price (P). Average I in sample is 5 and average P is Rs 8.9. Following regression was estimated: Î = 52.351 + 3.139 - 1 se = (37.39) (0.0187) df = 156, R? = 0.806 How would you interpret this model? Explain the shape of the curve. iv. What would be the slope and elasticity of number of installs with…
