   # Soccer Gear The East Coast College soccer team is planning to buy new gear for its road trip to California. The cost per shirt depends on the number of shirts the team orders as shown in the following table: Shirts Ordered x 5 25 40 100 125 Cost/Shirt A ( x ) ( $) 22.91 21.81 21.25 21.25 22.31 a. Which of the following functions best models the data? (A) A ( x ) = 0.005 x + 20.75 (B) A ( x ) = 0.01 x + 20 + 25 x (C) A ( x ) = 0.0005 x 2 − 0.07 x + 23.25 (D) A ( x ) = 25.5 ( 1.08 ) ( x − 5 ) b. Graph the model you chose in part (a) for 10 ≤ x ≤ 100 . Use your graph to estimate the lowest cost per shirt and the number of shirts the team should order to obtain the lowest price per shirt. BuyFindarrow_forward ### Finite Mathematics and Applied Cal... 7th Edition Stefan Waner + 1 other Publisher: Cengage Learning ISBN: 9781337274203 #### Solutions Chapter Section BuyFindarrow_forward ### Finite Mathematics and Applied Cal... 7th Edition Stefan Waner + 1 other Publisher: Cengage Learning ISBN: 9781337274203 Chapter 1.2, Problem 47E Textbook Problem 1 views ## Soccer Gear The East Coast College soccer team is planning to buy new gear for its road trip to California. The cost per shirt depends on the number of shirts the team orders as shown in the following table: Shirts Ordered x 5 25 40 100 125 Cost/Shirt A ( x ) ($ ) 22.91 21.81 21.25 21.25 22.31 a. Which of the following functions best models the data?(A) A ( x ) = 0.005 x + 20.75 (B) A ( x ) = 0.01 x + 20 + 25 x (C) A ( x ) = 0.0005 x 2 − 0.07 x + 23.25 (D) A ( x ) = 25.5 ( 1.08 ) ( x − 5 ) b. Graph the model you chose in part (a) for 10 ≤ x ≤ 100 . Use your graph to estimate the lowest cost per shirt and the number of shirts the team should order to obtain the lowest price per shirt.

(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(x) ($) 22.91 21.81 21.25 21.25 22.31 The options are: A(x)=0.005x+20.75 A(x)=0.01x+20+25x A(x)=0.0005x20.07x+23.25 A(x)=25.5(1.08)(x5) ### Explanation of Solution Given Information: The table shows the cost per shirt that depends on the number of shirts orders by the soccer team of the East Coast College who is planning to buy new gear for its road trip to California.  Shirts Ordered x 5 25 40 100 125 Cost/Shirt A(x) ($) 22.91 21.81 21.25 21.25 22.31

The options are:

A(x)=0.005x+20.75

A(x)=0.01x+20+25x

A(x)=0.0005x20.07x+23.25

A(x)=25.5(1.08)(x5)

Consider the function,

A(x)=0.005x+20.75

Evaluate the cost when number of shirts x=5 as;

A(5)=0.005(5)+20.75=0.025+20.75=20.775

Evaluate the cost when number of shirts x=25 as;

A(25)=0.005(25)+20.75=0.125+20.75=20.875

Evaluate the cost when number of shirts x=40 as;

A(40)=0.005(40)+20.75=0.2+20.75=20.95

Evaluate the cost when number of shirts x=100 as;

A(100)=0.005(100)+20.75=0.5+20.75=21.25

Evaluate the cost when number of shirts x=125 as;

A(125)=0.005(125)+20.75=0.625+20.75=21.375

Now, consider the function,

A(x)=0.01x+20+25x

Evaluate the cost when number of shirts x=5 as;

A(5)=0.01(5)+20+255=0.05+20+5=25.05

Evaluate the cost when number of shirts x=25 as;

A(25)=0.01(25)+20+2525=0.25+20+1=21.25

Evaluate the cost when number of shirts x=40 as;

A(40)=0.01(40)+20+2540=0.4+20+0.625=21.025

Evaluate the cost when number of shirts x=100 as;

A(100)=0.01(100)+20+25100=1+20+0.25=21.25

Evaluate the cost when number of shirts x=125 as;

A(125)=0.01(125)+20+25125=1.25+20+0.2=21.45

Now, consider the function,

A(x)=0.0005x20.07x+23.25

Evaluate the cost when number of shirts x=5 as;

A(5)=0.0005(5)20.07(5)+23.25=0.0005×250.35+23.25=0.01250.35+23.25=22.9125

Evaluate the cost when number of shirts x=25 as;

A(25)=0.0005(25)20.07(25)+23.25=0.0005×6251.75+23.25=0.31251.75+23.25=21.8125

Evaluate the cost when number of shirts x=40 as;

A(40)=0

(b)

To determine

To graph: The model obtained in part (a), for (10x100) 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(x) (\$) 22.91 21.81 21.25 21.25 22.31

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