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The U.S. national debtis the measure that captures all the federal government's outstanding debt, measured by outstanding bills, notes, bonds, and other debt instruments of the U.S. government. For years politicians have talked about a balanced federal budget. This is frequently a hot political topic. In this project, students will use mathematics and regression analysis to investigate the U.S. national debt. 1. The table below gives the U.S. national debt for September 30th from 1970 to 2022 . Create a scatterplo for this data and insert the scatterplot in your report.Let x be the number of years after 1970. Do not use the years themselves for x. 2. The scatterplot should show a pattern that increases gradually at first, then starts to level out a bit, but eventually starts to grow faster again. Perform a "quadratic regression" using your calculator, Desmos or Excel. Record the resulting regression equation and insert a copy of the graph of the function overlaid on top of a new graph of the scatterplot.This graph should be separate from the graph you created in step 1 above. Round coefficients and constants to four decimal places where possible. 3. Now perform an "exponential regression". Record the resulting regression equation and include a new graph of the function overlaid on the scatterplot. This graph should be separate from the previous graphs that you have created. Again, round coefficients and constants to four decimal places where possible. 4. Perform a "cubic regression". Record the resulting regression equation and include a new graph of the function overlaid on a new graph of the scatterplot. Round coefficients and constants to four decimal places where possible. 5. Which model (quadratic, exponential or cubic) do you think fits the data points best? Explain. 6. What will the national debt be over each of the next five years (20232027) according to each of the three models? Organize your answers in a table. 7. Use each model (exponential, quadratic and cubic) to predict when the national debt willdouble from its September 2022 level of 31,164.0 billion dollars. Which model do you think may be best at making this difficult prediction?Explain. 8. Reflection. Write a summary (1 or 2 paragraphs is fine) reflecting on what you have learned in this project. The U.S. national debtis the measure that captures all the federal government's outstanding debt, measured by outstanding bills, notes, bonds, and other debt instruments of the U.S. government. For years politicians have talked about a balanced federal budget. This is frequently a hot political topic. In this project, students will use mathematics and regression analysis to investigate the U.S. national debt. 1. The table below gives the U.S. national debt for September 30th from 1970 to 2022 . Create a scatterplo for this data and insert the scatterplot in your report.Let x be the number of years after 1970. Do not use the years themselves for x. 2. The scatterplot should show a pattern that increases gradually at first, then starts to level out a bit, but eventually starts to grow faster again. Perform a "quadratic regression" using your calculator, Desmos or Excel. Record the resulting regression equation and insert a copy of the graph of the function overlaid on top of a new graph of the scatterplot.This graph should be separate from the graph you created in step 1 above. Round coefficients and constants to four decimal places where possible. 3. Now perform an "exponential regression". Record the resulting regression equation and include a new graph of the function overlaid on the scatterplot. This graph should be separate from the previous graphs that you have created. Again, round coefficients and constants to four decimal places where possible. 4. Perform a "cubic regression". Record the resulting regression equation and include a new graph of the function overlaid on a new graph of the scatterplot. Round coefficients and constants to four decimal places where possible. 5. Which model (quadratic, exponential or cubic) do you think fits the data points best? Explain. 6. What will the national debt be over each of the next five years (20232027) according to each of the three models? Organize your answers in a table. 7. Use each model (exponential, quadratic and cubic) to predict when the national debt willdouble from its September 2022 level of 31,164.0 billion dollars. Which model do you think may be best at making this difficult prediction?Explain. 8. Reflection. Write a summary (1 or 2 paragraphs is fine) reflecting on what you have learned in this project
