Chapter 8.5, Problem 21STP

To determine

To find:the best prediction for the cost of $21$ cookies

Answer to Problem 21STP

Therefore, the correct option is B.

Explanation of Solution

Given:

  

  $\$5.00$

  $\$5.50$

  $\$5.25$

  $\$5.75$

Calculation:

Consider the table shows the relationship between cost of cookies and number of cookies.

Number of cookies   $(x)$	Cost   $(y)$
$0$	$0$
$2$	$0.5$
$6$	$1.5$
$8$	$2.0$

In order to find the equation that relates to the cost and number of cookies, first find constant rate of change.

So, take any two points and use the formula for rate of change.

  $Rateofchange=\frac{changeiny}{changein\text{ x}}$

It means rate of change is change in cost with respect to change in number of cookies.

So, consider two points as: $(2,0,5)$ and $(6,1,5)$

Thus, constant rate of change is:

  $\begin{array}{l}Rateofchange=\frac{1.5-0.5}{6-2}\\ =\frac{1}{4}\\ =0.25\end{array}$

Hence, the equation is $y=kx$ , that is , $y=0.25x$

To find the cost of $21$ cookies, put the value of $x=21$ in equation.

  $\begin{array}{l}y=0.25(21)\\ =5.25\end{array}$

Conclusion:

Therefore, the correct option is B.