   # Hockey Gear The South Coast College hockey team wants to purchase wool hats for its road trip to Alaska. The cost per hat depends on the number of hats the team orders as shown in the following table: Hats Ordered x 5 25 40 100 125 Cost/Hat A ( x ) ( $) 25.50 23.50 24.63 30.25 32.70 a. Which of the following functions best models the data? (A) A ( x ) = 0.05 x + 20.75 (B) A ( x ) = 0.1 x + 20 + 25 x (C) A ( x ) = 0.0008 x 2 − 0.07 x + 23.25 (D) A ( x ) = 25.5 ( 1.08 ) ( x − 5 ) b. Graph the model you chose in part (a) with 5 ≤ x ≤ 30 . 30. Use your graph to estimate the lowest cost per hat and the number of hats the team should order to obtain the lowest price per hat. BuyFindarrow_forward ### Finite Mathematics 7th Edition Stefan Waner + 1 other Publisher: Cengage Learning ISBN: 9781337280426 #### Solutions Chapter Section BuyFindarrow_forward ### Finite Mathematics 7th Edition Stefan Waner + 1 other Publisher: Cengage Learning ISBN: 9781337280426 Chapter 1.2, Problem 48E Textbook Problem 1 views ## Hockey Gear The South Coast College hockey team wants to purchase wool hats for its road trip to Alaska. The cost per hat depends on the number of hats the team orders as shown in the following table: Hats Ordered x 5 25 40 100 125 Cost/Hat A ( x ) ($ ) 25.50 23.50 24.63 30.25 32.70 a. Which of the following functions best models the data?(A) A ( x ) = 0.05 x + 20.75 (B) A ( x ) = 0.1 x + 20 + 25 x (C) A ( x ) = 0.0008 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) with 5 ≤ x ≤ 30 . 30. Use your graph to estimate the lowest cost per hat and the number of hats the team should order to obtain the lowest price per hat.

(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(x) ($) 25.5 23.5 24.63 30.25 32.7 The options are: A(x)=0.05x+20.75 A(x)=0.1x+20+25x A(x)=0.0008x20.07x+23.25 A(x)=25.5(1.08)(x5) ### Explanation of Solution Given Information: The table shows the cost per shirt that depends on the number of shirts orders by the soccer team of the East Coast College who is planning to buy new gear for its road trip to California.  Hats Ordered x 5 25 40 100 125 Cost/Hat A(x) ($) 25.5 23.5 24.63 30.25 32.7

The options are:

A(x)=0.05x+20.75

A(x)=0.1x+20+25x

A(x)=0.0008x20.07x+23.25

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

Consider the function, A(x)=0.05x+20.75

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

A(5)=0.05(5)+20.75=0.25+20.75=21

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

A(25)=0.05(25)+20.75=1.25+20.75=22

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

A(40)=0.05(40)+20.75=2+20.75=22.75

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

A(100)=0.05(100)+20.75=5+20.75=25.75

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

A(125)=0.05(125)+20.75=6.25+20.75=27

Now, consider the function,

A(x)=0.1x+20+25x

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

A(5)=0.1(5)+20+255=0.5+20+5=25.5

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

A(25)=0.1(25)+20+2525=2.5+20+1=23.5

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

A(40)=0.1(40)+20+2540=4+20+0.625=24.625

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

A(100)=0.1(100)+20+25100=10+20+0.25=30.25

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

A(125)=0.1(125)+20+25125=12.5+20+0.2=32.7

Now, consider the function,

A(x)=0.0008x20.07x+23.25

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

A(5)=0.0008(5)20.07(5)+23.25=0.0008×250.35+23.25=0.020.35+23.25=22.92

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

A(25)=0.0008(25)20.07(25)+23.25=0.0008×6251.75+23.25=0.51.75+23.25=22

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 (5x30) 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(x) (\$) 25.5 23.5 24.63 30.25 32.7

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