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approximated by the exponential function f(t) = 30 e0072t, where t is time in years, and t=0 corresponds to the year 2000. a) Given f(0) is 1375(billion) use this to write the parent equation in part b. b) In the equation f(t), replace yo with the initial debt. Write the exponential function that models this situation. c) If the total debt was 1375 billion in the year 2000 (year 0), find the total amount of debt for 2010. d) If the total debt was 1375 billion in the year 2000 (year 0), find the total amount of debt for 2021. e) Use desmos.com to graph the function and verify that your answers (coordinates) are on the graph.

approximated by the exponential function f(t) = 30 e0072t, where t is time in years, and t=0 corresponds to the year 2000. a) Given f(0) is 1375(billion) use this to write the parent equation in part b. b) In the equation f(t), replace yo with the initial debt. Write the exponential function that models this situation. c) If the total debt was 1375 billion in the year 2000 (year 0), find the total amount of debt for 2010. d) If the total debt was 1375 billion in the year 2000 (year 0), find the total amount of debt for 2021. e) Use desmos.com to graph the function and verify that your answers (coordinates) are on the graph.

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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Total debt: In a certain country, the amount of debt across all sectors (in billions of dollars) can be approximated by the exponential function. f(t) = 30e0.072, where t is time in years, and t=0 corresponds to the year 2000. a) Given f(0) is 1375(billion) use this to write the parent equation in part b. b) In the equation f(t), replace yo with the initial debt. Write the exponential function that models this situation. c) If the total debt was 1375 billion in the year 2000 (year 0), find the total amount of debt for 2010. d) If the total debt was 1375 billion in the year 2000 (year 0), find the total amount of debt for 2021. e) Use desmos.com to graph the function and verify that your answers (coordinates) are on the graph.
Transcribed Image Text:Total debt: In a certain country, the amount of debt across all sectors (in billions of dollars) can be approximated by the exponential function. f(t) = 30e0.072, where t is time in years, and t=0 corresponds to the year 2000. a) Given f(0) is 1375(billion) use this to write the parent equation in part b. b) In the equation f(t), replace yo with the initial debt. Write the exponential function that models this situation. c) If the total debt was 1375 billion in the year 2000 (year 0), find the total amount of debt for 2010. d) If the total debt was 1375 billion in the year 2000 (year 0), find the total amount of debt for 2021. e) Use desmos.com to graph the function and verify that your answers (coordinates) are on the graph.
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