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1.The cost for almost every aspect of health care in the U.S. has risen dramatically over the last 40 years. One of the central issues in the ongoing debate about containing health care costs is the amount of federal dollars spent on Medicare. Medicare is a federal program that, since 1966, has provided two coordinated plans for nearly all citizens age 65 or over. The shape of this graph suggests that an exponential function will model Medicare expenses fairly well. The data shown in the graph is from the U.S. Bureau of the Census as shown in The Statistical Abstract of the U.S. 1999. It gives Medicare expenses in billions of dollars

1.The cost for almost every aspect of health care in the U.S. has risen dramatically over the last 40 years. One of the central issues in the ongoing debate about containing health care costs is the amount of federal dollars spent on Medicare. Medicare is a federal program that, since 1966, has provided two coordinated plans for nearly all citizens age 65 or over. The shape of this graph suggests that an exponential function will model Medicare expenses fairly well. The data shown in the graph is from the U.S. Bureau of the Census as shown in The Statistical Abstract of the U.S. 1999. It gives Medicare expenses in billions of dollars

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Group Problems:** 1. The cost for almost every aspect of healthcare in the U.S. has risen dramatically over the last 40 years. One of the central issues in the ongoing debate about containing healthcare costs is the amount of federal dollars spent on Medicare. Medicare is a federal program that, since 1966, has provided two coordinated plans for nearly all citizens age 65 or over. The shape of this graph suggests that an exponential function will model Medicare expenses fairly well. The data shown in the graph is from the U.S. Bureau of the Census as shown in *The Statistical Abstract of the U.S. 1999*. It gives Medicare expenses in billions of dollars. | Year | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | |------|------|------|------|------|------|------| | Medicare expenses in billions of $ | 7.7 | 16.4 | 37.5 | 72.2 | 112.1 | 184.2 | **Figure 5.12** Medicare expenditures (in billions of dollars). Source: U.S. Bureau of the Census, *The Statistical Abstract of the United States, 1999*. - **Graph Explanation:** - The graph is a scatter plot displaying Medicare expenditures from 1970 to 1995. - The x-axis represents the years, ranging from 1970 to 2000. - The y-axis represents the Medicare expenses in billions of dollars, ranging from 0 to 250. - Data points are marked for each year listed in the table, showing an upward trend indicative of exponential growth. **Questions:** a. Use the regression capabilities of your technology to find the equation that best approximates the Medicare data given in the table above. Use four decimal places in your base B. Remember the exponential model is \( y = A(B)^t \). Define your variables. b. Write a sentence explaining what your base number B tells us about Medicare expenses. c. Does your model overestimate or underestimate Medicare expenses in 1970? By how much? d. Use your model to predict Medicare expenses for this year. Show how you got your answer. e. Now round the base B in your model to two decimal places. Using this new value, how much does your prediction of this year’s Medicare expenses change?
Transcribed Image Text:**Group Problems:** 1. The cost for almost every aspect of healthcare in the U.S. has risen dramatically over the last 40 years. One of the central issues in the ongoing debate about containing healthcare costs is the amount of federal dollars spent on Medicare. Medicare is a federal program that, since 1966, has provided two coordinated plans for nearly all citizens age 65 or over. The shape of this graph suggests that an exponential function will model Medicare expenses fairly well. The data shown in the graph is from the U.S. Bureau of the Census as shown in *The Statistical Abstract of the U.S. 1999*. It gives Medicare expenses in billions of dollars. | Year | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | |------|------|------|------|------|------|------| | Medicare expenses in billions of $ | 7.7 | 16.4 | 37.5 | 72.2 | 112.1 | 184.2 | **Figure 5.12** Medicare expenditures (in billions of dollars). Source: U.S. Bureau of the Census, *The Statistical Abstract of the United States, 1999*. - **Graph Explanation:** - The graph is a scatter plot displaying Medicare expenditures from 1970 to 1995. - The x-axis represents the years, ranging from 1970 to 2000. - The y-axis represents the Medicare expenses in billions of dollars, ranging from 0 to 250. - Data points are marked for each year listed in the table, showing an upward trend indicative of exponential growth. **Questions:** a. Use the regression capabilities of your technology to find the equation that best approximates the Medicare data given in the table above. Use four decimal places in your base B. Remember the exponential model is \( y = A(B)^t \). Define your variables. b. Write a sentence explaining what your base number B tells us about Medicare expenses. c. Does your model overestimate or underestimate Medicare expenses in 1970? By how much? d. Use your model to predict Medicare expenses for this year. Show how you got your answer. e. Now round the base B in your model to two decimal places. Using this new value, how much does your prediction of this year’s Medicare expenses change?
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