Question
(a) Find an exponential model for the federal debt, based on the data in the table." Let $x=0$ correspond to 1960(b) Use the model to estimate the federal debt in 2010 .(TABLE CAN NOT COPY)
Step 1
We let $x=0$ correspond to 1960. We input our $x$ values into $x_1$ and our $y$ values (the federal debt in billions of dollars) into $y_1$. Show more…
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The following table shows the federal debt for a short period of time from 1980 to 1991. Years Federal Debt (in trillions) 1980 .909 1981 .994 1982 1.1 1983 1.4 1984 1.6 1985 1.8 1986 2.1 1987 2.3 1988 2.6 1989 2.9 1990 3.2 1991 3.6 1.) Determine if the data is linear or exponential and explain how you reached your conclusion. 2.) Perform exponential regression and generate an equation that predicts the federal debt based on the year 3.) Find the residual for this model for the year 1990 4.) Use this model to predict the national debt for the year 2000.
The total public debt $D$ (in trillions of dollars) in the United States from 2005 through 2014 can be approximated by the model $$D=0.051 t^{2}+0.20 t+5.0, \quad 5 \leq t \leq 14$$ 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.
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Let $D(t)$ be the US national debt at time $t .$ The table gives approximate values of the function by providing end of year estimates, in billions of dollars, from 1990 to $2010 .$ Interpret and estimate the value of $D^{\prime}(2000) .$ $$\begin{array}{|c|c|c|c|c|c|}\hline t & {1990} & {1995} & {2000} & {2005} & {2010} \\ \hline D(t) & {3233} & {4974} & {5662} & {8170} & {14,025} \\ \hline\end{array}$$
Derivatives
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