The numbers of polio cases in the world are shown in the table for various years. Year Number of Polio Cases (thousands) 1988 350 1992 138 1996 36 2000 4 2005 3.2 2007 1.3 Let f(t) be the number of polio cases in thousands t years since 1980. Use a graphing calculator to draw a scattergram of the data. Is it better to model the data by using a linear or exponential model? If you use Desmos to find an exponential model, do not forget the check the LOG Mode Box. Exponential Find an equation of f. Hint 了(t) Round the coefficients to 4 decimal places. The number of polio cases is Select an answer v by Select an answer ♥ per year. Predict the number of polio cases in 2019. Hint Predict in whích year there will be 1 case of polio. Hint Find the approximate half-life of the number of polio cases. Hint years

The numbers of polio cases in the world are shown in the table for various years. Year Number of Polio Cases (thousands) 1988 350 1992 138 1996 36 2000 4 2005 3.2 2007 1.3 Let f(t) be the number of polio cases in thousands t years since 1980. Use a graphing calculator to draw a scattergram of the data. Is it better to model the data by using a linear or exponential model? If you use Desmos to find an exponential model, do not forget the check the LOG Mode Box. Exponential Find an equation of f. Hint 了(t) Round the coefficients to 4 decimal places. The number of polio cases is Select an answer v by Select an answer ♥ per year. Predict the number of polio cases in 2019. Hint Predict in whích year there will be 1 case of polio. Hint Find the approximate half-life of the number of polio cases. Hint years

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.1: Logistic Functions

Problem 16E: Cable TV The following table shows the number C. in millions, of basic subscribers to cable TV in...

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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?
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?
Cable TV The following table shows the number C. in millions, of basic subscribers to cable TV in the indicated year These data are from the Statistical Abstract of the United States. Year 1975 1980 1985 1990 1995 2000 C 9.8 17.5 35.4 50.5 60.6 60.6 a. Use regression to find a logistic model for these data. b. By what annual percentage would you expect the number of cable subscribers to grow in the absence of limiting factors? c. The estimated number of subscribers in 2005 was 65.3million. What light does this shed on the model you found in part a?