Chapter 1.2, Problem 47E

(a)

To determine

The correct function that best fits the data provided in the table that shows the cost per shirt that depends on the number of shirts orders by the soccer team of the East Coast College who is planning to buy new gear for its road trip to California.

Shirts Ordered x	$5$	$25$	$40$	$100$	$125$
Cost/Shirt $A\left(x\right)$ $\left(\$\right)$	$22.91$	$21.81$	$21.25$	$21.25$	$22.31$

The options are:

$A\left(x\right)=0.005x+20.75$

$A\left(x\right)=0.01x+20+\frac{25}{x}$

$A\left(x\right)=0.0005x^2-0.07x+23.25$

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

(b)

To determine

To graph: The model obtained in part (a), for $\left(10\le x\le 100\right)$ and estimate the minimum cost per shirt and also number of shirts the team must order to obtain the lowest price per shirt using the graph where the table that shows the cost per shirt that depends on the number of shirts orders by the soccer team of the East Coast College who is planning to buy new gear for its road trip to California.

Shirts Ordered x	$5$	$25$	$40$	$100$	$125$
Cost/Shirt $A\left(x\right)$ $\left(\$\right)$	$22.91$	$21.81$	$21.25$	$21.25$	$22.31$