37. In the previous question, the scientist decides to reverse the plot. 120.0 49.5 20.4 8.4 Amount of XUranium (mg) Y minutes -40 10+ 10 20 . 30 0 a) Create a scatter plot, and draw a curve of best fit for the data using logartihmic regression. -130+-- Yarbinx1 - 120+ -110+ 100+ --90+ -80 --70- --60- 40 SD " 30 60 7D 60 80 90 100 110 120 130 . 90 x=66 3.5 120 Y=162₂356-33.9242 In b) Use your regression equation to estimate the half-life of uranium-239. This is the time for the amount of uranium 239 to drop by 50%. 23.459.mg (60,23.459)

What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?

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?

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?