Modeling Data The table shows the net receipts anil the amounts required to ser\ ice the

Chapter 5, Problem 70

(choose chapter or problem)

Modeling Data The table shows the net receipts anil the amounts required to ser\ ice the nation.il debt of the United .States liom 1990 through 1999. The nionetaiy amounts are given in billions (if dollars. iSaurce: U.S. Oflicc <>IMiiihii;ciiieiil iiiul Hikl!>cn Year 1990 1991 1992 1993 1994 Receipts l(B2.0 1055.0 1091.3 1 1 .54.4 1258.6 Interest 264.7 285.5 292.3 292.5 296.3 Year 1995 1996 1997 1998 1999 Receipts l-\5|.8 1453.1 1579.3 1721.8 1 806.3 Interest 332.4 344.0 355.8 363.8 353.4 (a) Use the regression ciiiabilities of a graphing utility to find an exponential model R for the receipts and a quartic model / for the amount required to service the debt. Let t represeni the time in years, with / = concsponding to 1990. (hi Use a graphing utility to plot the points corresponding to the receipts, and graph the corresponding model. Based on the model, what is the continuous rate of growth of the receipts? (c) Use a graphing utility to plot the points corresponding to the amount required to service the debt, and graph the quartic model. (d) Find a function Pit) that approximates the percent of the receipts that is required to service the national debt. Use a graphing utility to graph this function.