Question

8. The table below shows college textbook sales in the U.S. from 2000 to 2005.YearTextbook Sales (millions of dollars)200042652001457120024899200350862004547920055703(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.Pt = (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

Recall that the quadratic model is given by

`P(t)=At^2+Bt+C`

Where A, B, and C are the coefficients.

t is the time in years t = 0 in 2000

(a) Let us use any online calculator to find the values of the coefficients for the quadratic model.

Enter the data values into the calculator from the given in the table.

So, the values of the coefficients are (rounded to 2 decimal places)

A = -2.68

B = 301.99

C = 4270.07

Therefore, the equation of the quadratic model is

`P(t)=-2.68t^2+301.99t+4270.07`

(b)

2015 means t = 15

Substitute t = 15 into the above quadratic equation

`\begin{gathered} P(t)=-2.68t^2+301.99t+4270.07 \\ P(15)=-2.68(15)^2+301.99(15)+4270.07 \\ P(15)=-603^{}+4529.85+4270.07 \\ P\mleft(15\mright)=8197 \end{gathered}`

Therefore, you should expect 8197 million dollars to be spent on college textbooks in 2015.

(c)

We need to substitute P(t) = 7000 million dollars into the quadratic equation and solve for t

`\begin{gathered} 7000=-2.68t^2+301.99t+4270.07 \\ -2.68t^2+301.99t+4270.07-7000=0 \\ -2.68t^2+301.99t-2729.93=0 \end{gathered}`

Solve the above equation using the calculator

We get the following two values for t

t = 9.91 and 102.77

Accept the smaller value and round it to the nearest whole number

t = 10 which means 2010

During the year 2010