Question

8. The table below shows college textbook sales in the U.S. from 2000 to 2005. Year Textbook Sales (millions of dollars) 2000 4265 2001 4571 2002 4899 2003 5086 2004 5479 2005 5703 (a) Use a graphing calculator or spreadsheet program to find a quadratic model that best fits this data. Let t represent the year, with t = 0 in 2000. Round each coefficient to two decimal places. P t = (b) Based on this model, how much would you expect to be spent on college textbooks in 2015? Round your answer to the nearest whole number. million dollars (c) When would you expect textbook sales to first reach $7 billion (7000 million dollars)? Give your answer as a calendar year (ex: 1997). During the year

Answer 1

We have been given a table that indicates Textbook sales (millions of dollars) from the year 2000 to 2005.

Method: Since we have been told to model the equation that best fits the data.

To do this, we have been told to let t represent the years.

We can also represent the textbook sales as Pt

Using a graphing calculator

Question A

Thus, the quadratic model that best fits this data is:

$P_t=-2.68t^2_{1^{^{^{}}\text{ }}}+301.99t_1+4270.07$

Question B

We are told to predict the Textbook sales in 2015

In 2015, the value of t1 will be

$\begin{gathered} t_1=2015-2000=15 \\ t_1=15 \end{gathered}$

We can now proceed to substitute

$t_1=15$

Into the equation

$\begin{gathered} P_t=-2.68\times15^2+301.99\times15+4270.07 \\ P_t=8196.92 \end{gathered}$

in 2015, we would expect

$P_t\approx8197\text{ million dollars}$

Thus, approximately 8197 million dollars is expected to be spent on college textbook

Question C

To predict when the total sales will be approximately $7billion,

We will take our value for

$P_t=7000$

This means that

$7000=-2.68t^2_{1^{^{^{}}\text{ }}}+301.99t_1+4270.07$

Thus, we will have to find the value of t1

Again, using the graph to predict when Pt = $7000

We can see from the graph that this value is about 9.952 years

So we will try when

$\begin{gathered} t_1=9\text{years} \\ \text{and when} \\ t_1=10\text{years} \end{gathered}$

Using the model

$P_t=-2.68t^2_{1^{^{^{}}\text{ }}}+301.99t_1+4270.07$

When

$\begin{gathered} t_1=9\text{ years} \\ P_t=\text{ \ }6770.9 \end{gathered}$

When

$\begin{gathered} t_1=10 \\ P_t=\text{ \ 7021}.97 \end{gathered}$

Therefore, we can say that in approximately 10 years from 2000.

This means that in the year 2010, we would expect textbook sales to first reach $7 billion