(a)
To calculate: The function for the instantaneous rate of change of the number of beneficiaries, if the function for the number of beneficiaries (in millions) t years past 1950 model as
Year | Number of Beneficiaries (millions) | Year | Number of Beneficiaries (millions) |
1950 | 2.9 | 2000 | 44.8 |
1960 | 14.3 | 2010 | 53.3 |
1970 | 25.2 | 2020 | 68.8 |
1980 | 35.1 | 2030 | 82.7 |
1990 | 39.5 |
(b)
To calculate: The instantaneous rate of change of the number of beneficiaries in 2020 and its interpretation, if the function for the number of beneficiaries (in millions) t years past 1950 model as
The data that gives the number of Social Security beneficiaries (actual and projected) for selected years from 1950 through 2030 for which the function is modeled is tabulated below
Year | Number of Beneficiaries (millions) | Year | Number of Beneficiaries (millions) |
1950 | 2.9 | 2000 | 44.8 |
1960 | 14.3 | 2010 | 53.3 |
1970 | 25.2 | 2020 | 68.8 |
1980 | 35.1 | 2030 | 82.7 |
1990 | 39.5 |
(c)
The time range among (from 2010 to 2020, from 2020 to 2030 orfrom 2010 to 2030) for which the average rate of change is the best approximates of the instantaneous rate of change in 2020, if the function for the number of beneficiaries (in millions) t years past 1950 model as
The data that gives the number of Social Security beneficiaries (actual and projected) for selected years from 1950 through 2030 for which the function is modeled is tabulated below
Year | Number of Beneficiaries (millions) | Year | Number of Beneficiaries (millions) |
1950 | 2.9 | 2000 | 44.8 |
1960 | 14.3 | 2010 | 53.3 |
1970 | 25.2 | 2020 | 68.8 |
1980 | 35.1 | 2030 | 82.7 |
1990 | 39.5 |
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Mathematical Applications for the Management Life and Social Sciences
- Cigarette Smokers The following table gives a recent estimate in millions of the smoking status among persons 25 years of the age and over their highest level of education. Source: National health interview survey. Education Current smoker Former smoker Non smoker Total Less than a high school diploma 7.90 6.66 14.12 28.68 High school diploma or GED 14.38 13.09 25.70 53.17 Some collage 12.41 13.55 28.65 54.61 Bachelors degree or higher 4.97 12.87 38.34 56.18 Total 39.66 46.17 106.81 192.64 a. Find the probability that a person is a current smoker. b. Find a probability that a person has less than a high school diploma. c. Find a probability that a person is a current smoker and has less than a high school diploma. d. Find the probability that a person is a current smoker, given that the person has less than a high school diploma. e. Are the events current smoker and less than a high school diploma independent events?arrow_forwardOil ProductionThe following table shows the amount of crude oil in billions of barrels produced in the United States in recent years. Source: U.S. Energy Information Administration. Year Crude Oil Produced 2002 2.097 2003 2.060 2004 1.989 2005 1.893 2006 1.857 2007 1.853 2008 1.830 2009 1.954 2010 2.000 2011 2.063 2012 2.377 In this exercise we are interested in the total amount of crude oil produced over the 10-year period from mid-2002 to mid-2012, using the data for the 11 years above. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation. Approximate the amount of crude oil produced over the 10-year period 2002-2012 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a. This is also equivalent to a formula known as the trapezoidal rule, discussed in the next chapter. If your calculator has a cubic regression feature, find the best-fitting cubic function for these data, letting t=0 correspond to 2000. Then integrate this equation over the interval [2.12] to estimate the amount of crude oil produced over this time period. Compare with your answer to part a.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,