Chapter 9.7, Problem 22PPE

To determine

To graph:

The given equation data suggests a type of function for use and equation fit the data exactly.

Answer to Problem 22PPE

  

With the help of the graph it is showed that the equation may not fit the data exactly.

Explanation of Solution

Given information:

Day	Visitors
$1$	$52$
$2$	$197$
$3$	$447$
$4$	$805$
$5$	$1270$

Graph:

Following is the data that represents the number of visitor’s website:

Day $\left(x\right)$	Visitors$\left(y\right)$
$1$	$52$
$2$	$197$
$3$	$447$
$4$	$805$
$5$	$1270$

Following graph is drawn with the help of above table:

  

Interpretation:

Observe that the graph shows a parabolic curve hence is quadratic in nature

Day $\left(x\right)$	$1$	$2$	$3$	$4$	$5$
Visitors $\left(y\right)$	$52$	$197$	$447$	$805$	$1270$
First Common Difference	---	$197-52=145$	$447-197=250$	$805-447=358$	$1270-52=145$
Second Common Difference	---	---	$250-145=105$	$358-250=108$	$465-358=107$

From the graph a quadratic function fits the data

Hence, an equation of the type $y=a{x}^2+bx+c$ fits the data.

Observe that the second common difference is not exactly same.

Hence the equation may not fit the data exactly.