Chapter 1.2, Problem 48E

(a)

To determine

The correct function that best fits the data provided in the table that shows the cost per hat that depends on the number of hats orders by the hockey team of the South Coast College who is planning to buy wool hats for its road trip to Alaska.

Hats Ordered x	$5$	$25$	$40$	$100$	$125$
Cost/Hat $A\left(x\right)$ $\left(\$\right)$	$25.50$	$23.50$	$24.63$	$30.25$	$32.70$

The options are:

$A\left(x\right)=0.05x+20.75$

$A\left(x\right)=0.1x+20+\frac{25}{x}$

$A\left(x\right)=0.0008x^2-0.07x+23.25$

$A\left(x\right)=25.5{\left(1.08\right)}^{\left(x-5\right)}$

(b)

To determine

To graph: The model obtained in part (a), for $\left(5\le x\le 30\right)$ and estimate the minimum cost per hat and also number of hats the team must order to obtain the lowest price per shirt using the graph where the table that shows the cost per hat that depends on the number of hats orders by the hockey team of the South Coast College who is planning to buy new wool hats for its road trip to Alaska.

Hats Ordered x	$5$	$25$	$40$	$100$	$125$
Cost/Hat $A\left(x\right)$ $\left(\$\right)$	$25.50$	$23.50$	$24.63$	$30.25$	$32.70$