Chapter 8.1, Problem 36PPS

(a)

To determine

To calculate: To find if the set of ordered pairs (year, whole milk) is a function

Answer to Problem 36PPS

The set of ordered pairs (year, whole milk) is a function

Explanation of Solution

Given information: Table showing the sales of milk in the U.S in different years

U.S Milk Sales 1960-2000
Year	Whole Milk	Reduced and Low fat milk
1960	42,999	389
1970	41,512	6,163
1980	31,253	15,918
1990	21,333	24,509
2000	18,448	23,649

Formula Used:

According to function rule, no input can have more than one output.

The set ordered pairs is referred to as function when no two ordered pairs have the same first coordinate with different second coordinate

Calculation:

Given the table showing the sales of milk in the U.S in different years

U.S Milk Sales 1960-2000
Year	Whole Milk	Reduced and Low fat milk
1960	42,999	389
1970	41,512	6,163
1980	31,253	15,918
1990	21,333	24,509
2000	18,448	23,649

Set of ordered pairs of (year, whole milk)is represented as below

  $\left\{\left(1960,42999\right),\left(1970,41512\right),\left(1980,31253\right),\left(1990,21333\right),\left(2000,18448\right)\right\}$

Here, no two ordered pairs have same first coordinate.

Thus, the set of ordered pairs is a function

Conclusion:

Hence, the set of ordered pairs (year, whole milk) is a function

(b)

To determine

To calculate: To find if the set of ordered pairs (year, Reduced and low-fat milk) is a function

Answer to Problem 36PPS

The set of ordered pairs (year, Reduced and low-fat milk) is a function

Explanation of Solution

Given information: Table showing the sales of milk in the U.S in different years

U.S Milk Sales 1960-2000
Year	Whole Milk	Reduced and Low fat milk
1960	42,999	389
1970	41,512	6,163
1980	31,253	15,918
1990	21,333	24,509
2000	18,448	23,649

Formula Used:

According to function rule, no input can have more than one output.

The set ordered pairs is referred to as function when no two ordered pairs have the same first coordinate with different second coordinate

Calculation:

Given the table showing the sales of milk in the U.S in different years

U.S Milk Sales 1960-2000
Year	Whole Milk	Reduced and Low fat milk
1960	42,999	389
1970	41,512	6,163
1980	31,253	15,918
1990	21,333	24,509
2000	18,448	23,649

Set of ordered pairs of (year, Reduced and low-fat milk) is represented as below

  $\left\{\left(1960,389\right),\left(1970,6163\right),\left(1980,15918\right),\left(1990,24509\right),\left(2000,23649\right)\right\}$

Here, no two ordered pairs have same first coordinate.

Thus, the set of ordered pairs is a function

Conclusion:

Hence, the set of ordered pairs (year, Reduced and low-fat milk) is a function

(c)

To determine

To calculate: To describe the relationship between year and million pounds of whole milk purchased and describe the relationship between year and million pounds of reduced and low-fat milk purchased

Answer to Problem 36PPS

With the increase in year, purchase of whole milk has decreased and the purchase of reduced and low-fat milk has increased

Explanation of Solution

Given information: Table showing the sales of milk in the U.S in different years

U.S Milk Sales 1960-2000
Year	Whole Milk	Reduced and Low fat milk
1960	42,999	389
1970	41,512	6,163
1980	31,253	15,918
1990	21,333	24,509
2000	18,448	23,649

Calculation:

Given the table showing the sales of milk in the U.S in different years

U.S Milk Sales 1960-2000
Year	Whole Milk	Reduced and Low fat milk
1960	42,999	389
1970	41,512	6,163
1980	31,253	15,918
1990	21,333	24,509
2000	18,448	23,649

From above table,

As year increasing, the purchase of million pounds of whole milk is decreasing.

As year is increasing, the purchase of million pounds of reduced and low-fat milk is increasing

Conclusion:

Hence, with the increase in year, purchase of whole milk has decreased, and the purchase of reduced and low-fat milk has increased