The future of Social Security and Medicare generates a lot of debate and political posturing. Analysts predict that, without significant change, Social Security and Medicare funds will be exhausted at some future date (the date depends on the expert). The exercise asks you to use linear trends based on Social Security Administration historical data in order to estimate when, if ever, the funds will be in trouble (i.e., when disbursements will exceed income). Social Security income for the years 1990-2000 suggest that the income trend can be estimated by the equation y = 21.21x + 264.4 where x is the number of years since 1990 and y = annual income in billions of dollars, For the same years, the Social Security disbursements have the linear trend y = 13.28x + 226.54. (a) Find the point where income = disbursements. (Enter your answer as an ordered pair. Round your answers to two decimal places.) (х, у) - -4.77,163.23 (b) Does this suggest that Social Security is going broke? O Yes O No (c) What other factors might influence the trend that would cause it to deviate from the linear trend? The data for 1990 - 2003 is based on the populations that pay into the Social Security fund and those that secure payments from the fund. The relative size of these populations will change as Baby Boomers retire. The Baby Boomers are the generation for which there was a significantly higher birth rate. As they retire, the population of Social Security recipients will increase increase Thus, income will decrease vv and disbursements will v and those paying into the fund will decrease v This effect is not included in trends based on past income and disbursements.
The future of Social Security and Medicare generates a lot of debate and political posturing. Analysts predict that, without significant change, Social Security and Medicare funds will be exhausted at some future date (the date depends on the expert). The exercise asks you to use linear trends based on Social Security Administration historical data in order to estimate when, if ever, the funds will be in trouble (i.e., when disbursements will exceed income). Social Security income for the years 1990-2000 suggest that the income trend can be estimated by the equation y = 21.21x + 264.4 where x is the number of years since 1990 and y = annual income in billions of dollars, For the same years, the Social Security disbursements have the linear trend y = 13.28x + 226.54. (a) Find the point where income = disbursements. (Enter your answer as an ordered pair. Round your answers to two decimal places.) (х, у) - -4.77,163.23 (b) Does this suggest that Social Security is going broke? O Yes O No (c) What other factors might influence the trend that would cause it to deviate from the linear trend? The data for 1990 - 2003 is based on the populations that pay into the Social Security fund and those that secure payments from the fund. The relative size of these populations will change as Baby Boomers retire. The Baby Boomers are the generation for which there was a significantly higher birth rate. As they retire, the population of Social Security recipients will increase increase Thus, income will decrease vv and disbursements will v and those paying into the fund will decrease v This effect is not included in trends based on past income and disbursements.
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 3SE: The Oxford Dictionary defines the word nominal asa value that is “stated or expressed but...
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Transcribed Image Text:The future of Social Security and Medicare generates a lot of debate and political posturing. Analysts predict that, without significant change, Social Security and Medicare funds will
be exhausted at some future date (the date depends on the expert). The exercise asks you to use linear trends based on Social Security Administration historical data in order to
estimate when, if ever, the funds will be in trouble (i.e., when disbursements will exceed income).
Social Security income for the years 1990-2000 suggest that the income trend can be estimated by the equation
y = 21.21x + 264.4
where x is the number of years since 1990 and y = annual income in billions of dollars, For the same years, the Social Security disbursements have the linear trend
y = 13.28x + 226.54.
(a) Find the point where income = disbursements. (Enter your answer as an ordered pair. Round your answers to two decimal places.)
(х, у) -
-4.77,163.23
(b) Does this suggest that Social Security is going broke?
O Yes
O No
(c) What other factors might influence the trend that would cause it to deviate from the linear trend?
The data for 1990 - 2003 is based on the populations that pay into the Social Security fund and those that secure payments from the fund. The relative size of these
populations will change as Baby Boomers retire. The Baby Boomers are the generation for which there was a significantly higher birth rate. As they retire, the population of
Social Security recipients will increase
increase
Thus, income will decrease vv and disbursements will
v and those paying into the fund will decrease v
This effect is not included in trends based on past income and disbursements.
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