The total public debt D (in trillions of dollars) in the United States from 2005 through

Chapter 2, Problem 100

(choose chapter or problem)

The total public debt D (in trillions of dollars) in the United States from 2005 through 2014 can be approximated by the model

\(D=0.05 t^{2}+0.20 t+5.0,\ \ \ 5 \leq t \leq 14\)

where t represents the year, with t = 5 corresponding to 2005. (Source: U.S. Department of Treasury)

(a) Determine algebraically when the total public debt reached $10 trillion.

(b) Verify your answer to part (a) by creating a table of values for the model.

(c) Use a graphing utility to graph the model.

(d) Use the model to predict when the total public debt will reach $20 trillion.

(e) Do you believe the model could be used to predict the total public debt for years beyond 2014? Explain your reasoning.

Text Transcription:

D=0.051t^2 +0.20t+5.0, 5 leq t leq 14