Chapter 5, Problem 58RE

(a)

To determine

To graph: The scatter plot with academic years as the independent variable by using graphing utility, where the data in the following table represents the average in-state tuition and fees at public four year colleges and universities in the United States from academic year $1990-91$ to $2017-18$:

$\begin{array}{cc}\text{Academic}\text{year}& \begin{array}{l}\text{Tuition}\text{and}\text{fees}\\ \text{(in}\text{2017}\text{dollars)}\end{array}\\ 1990-91\left(x=0\right)& 3580\\ 1995-96\left(x=5\right)& 4510\\ 2000-01\left(x=10\right)& 4970\\ 2005-06\left(x=15\right)& 6880\\ 2009-10\left(x=19\right)& 8040\\ 2013-14\left(x=23\right)& 9310\\ 2017-18\left(x=27\right)& 9970\end{array}$

(b)

To determine

The exponential model using graphing utility, where the data in the following table represents the average in-state tuition and fees at public four year colleges and universities in the United States from academic year $1990-91$ to $2017-18$:

$\begin{array}{cc}\text{Academic}\text{year}& \begin{array}{l}\text{Tuition}\text{and}\text{fees}\\ \text{(in}\text{2017}\text{dollars)}\end{array}\\ 1990-91\left(x=0\right)& 3580\\ 1995-96\left(x=5\right)& 4510\\ 2000-01\left(x=10\right)& 4970\\ 2005-06\left(x=15\right)& 6880\\ 2009-10\left(x=19\right)& 8040\\ 2013-14\left(x=23\right)& 9310\\ 2017-18\left(x=27\right)& 9970\end{array}$

(c)

To determine

The function $y=(3610.268401){(1.040624942)}^x$ in the form of $A(t)=A_o{e}^{kt}$, where the data in the following table represents the average in-state tuition and fees at public four year colleges and universities in the United States from academic year $1990-91$ to $2017-18$:

$\begin{array}{cc}\text{Academic}\text{year}& \begin{array}{l}\text{Tuition}\text{and}\text{fees}\\ \text{(in}\text{2017}\text{dollars)}\end{array}\\ 1990-91\left(x=0\right)& 3580\\ 1995-96\left(x=5\right)& 4510\\ 2000-01\left(x=10\right)& 4970\\ 2005-06\left(x=15\right)& 6880\\ 2009-10\left(x=19\right)& 8040\\ 2013-14\left(x=23\right)& 9310\\ 2017-18\left(x=27\right)& 9970\end{array}$

(d)

To determine

To graph: The exponential function $A(t)=3610.268401e^{\left(0.03982\right)t}$ or $y=(3610.268401){(1.040624942)}^x$ on scatter plot, where data in the following table represents the average in-state tuition and fees at public four year colleges and universities in the United States from academic year $1990-91$ to $2017-18$:

$\begin{array}{cc}\text{Academic}\text{year}& \begin{array}{l}\text{Tuition}\text{and}\text{fees}\\ \text{(in}\text{2017}\text{dollars)}\end{array}\\ 1990-91\left(x=0\right)& 3580\\ 1995-96\left(x=5\right)& 4510\\ 2000-01\left(x=10\right)& 4970\\ 2005-06\left(x=15\right)& 6880\\ 2009-10\left(x=19\right)& 8040\\ 2013-14\left(x=23\right)& 9310\\ 2017-18\left(x=27\right)& 9970\end{array}$

(e)

To determine

The prediction of academic year when the average tuition will reach $\$16,000$, where data in the following table represents the average in-state tuition and fees at public four year colleges and universities in the United States from academic year $1990-91$ to $2017-18$:

$\begin{array}{cc}\text{Academic}\text{year}& \begin{array}{l}\text{Tuition}\text{and}\text{fees}\\ \text{(in}\text{2017}\text{dollars)}\end{array}\\ 1990-91\left(x=0\right)& 3580\\ 1995-96\left(x=5\right)& 4510\\ 2000-01\left(x=10\right)& 4970\\ 2005-06\left(x=15\right)& 6880\\ 2009-10\left(x=19\right)& 8040\\ 2013-14\left(x=23\right)& 9310\\ 2017-18\left(x=27\right)& 9970\end{array}$