Chapter 5.8, Problem 33PPSE

Solution

To determine : The reason for quadratic model being more appropriate for the given data.

The quadratic model is more appropriate for the given data because it shows an increasing trend.

Given information :

The table given below shows the number of students enrolled in a high school personal finance course.

Year	No. of Students Enrolled
$\begin{array}{l}2000\\ 2004\\ 2008\\ 2010\end{array}$	$\begin{array}{l}50\\ 65\\ 94\\ 110\end{array}$

A student says that a cubic model would best fit the data based on the $\left(n+1\right)$ Point Principle.

Explanation :

Construct quadratic and cubic model for this data using calculator and take 2000 as the base year, where $x=0$ .

The quadratic model will be $y=a{x}^2+bx+c$ .

The values are $a=0.35,b=2.60,c=49.77$ ; so the model will be:

  $y=0.35x^2+2.60x+49.77$

The graph of the model will be:

  

The cubic model will be $y=a{x}^3+b{x}^2+cx+d$ .

The values are $a=0.031,b=0.81,c=1,d=50$ .

So, the cubic model will be:

  $y=0.031x^3+0.81x^2+1x+50$

The graph of the model will be:

  

From the given table it can be observed that the number of students are increasing constantly and it is well represented by graph of the quadratic model.

Therefore, the quadratic model is more appropriate for the given data.