example 3 Blood Alcohol Percent

Chapter 1.4

The table gives the number of drinks and the resulting blood alcohol percent for a 180-lb man. (“One drink” is equal to 1.25 oz of 80 proof liquor, 12 oz of a regular beer, or 5 oz of table wine, and many states have set 0.08% as the legal limit for driving under the influence.)

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

2009 PBLPathways

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.09 0.07

4 30.02

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.09 0.07

4 30.02

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.09 0.07

4 30.02

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.09 0.07

4 30.02

percent per drink

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.11 0.09

5 40.02

percent per drink

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.13 0.11

6 50.02

percent per drink

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.15 0.13

7 60.02

percent per drink

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.17 0.15

8 70.02

percent per drink

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.19 0.17

9 80.02

percent per drink

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.21 0.19

10 90.02

percent per drink

2009 PBLPathways

a. Is the rate of change of the blood alcohol percent for a 180-lb man constant? What is it?

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

change in y valuesslope

change in x values

0.21 0.19

10 90.02

percent per drink

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

1 1

0.07 0.02 3

0.07 0.02 0.06

0.02 0.01

y y m x x

y x

y x

y x

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

1 1

0.07 0.02 3

0.07 0.02 0.06

0.02 0.01

y y m x x

y x

y x

y x

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

1 1

0.07 0.02 3

0.07 0.02 0.06

0.02 0.01

y y m x x

y x

y x

y x

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

1 1

0.07 0.02 3

0.07 0.02 0.06

0.02 0.01

y y m x x

y x

y x

y x

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

1 1

0.07 0.02 3

0.07 0.02 0.06

0.02 0.01

y y m x x

y x

y x

y x

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

0.02 0.02 0.01

y mx b

y x b y x

0.07 0.02 3

0.07 0.06

0.01

b

b

b

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

0.02 0.02 0.01

y mx b

y x b y x

0.07 0.02 3

0.07 0.06

0.01

b

b

b

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

0.02 0.02 0.01

y mx b

y x b y x

0.07 0.02 3

0.07 0.06

0.01

b

b

b

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

0.02 0.02 0.01

y mx b

y x b y x

0.07 0.02 3

0.07 0.06

0.01

b

b

b

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

0.02 0.02 0.01

y mx b

y x b y x

0.07 0.02 3

0.07 0.06

0.01

b

b

b

2009 PBLPathways

b. Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

Number of Drinks (x)

3 4 5 6 7 8 9 10

Blood Alcohol Percent (y)

0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21

0.02 0.02 0.01

y mx b

y x b y x

0.07 0.02 3

0.07 0.06

0.01

b

b

b