The percentage of U.S. households that own a VCR rose steadily since their introduction in the late 1970s. At right is a table showing the percentage of U.S. households that owned a VCR in various years (percentages rounded to the nearest hundredth).

The percentage can be modeled by the function

where P = the percentage of U.S. households that own a VCR and t = the number of years since 1978.

ENTER THE FUNCTION IN THE Y= MENU OF YOUR GRAPHING CALCULATOR.

Use the table options on your calculator to help answer the following questions:

1. Use functional notation to represent percentage of U.S. households that owned a VCR in 1992 and determine that number. Answer to the nearest hundredth.

2. Explain what is meant by P(0), and find its value.

3. Based on the model, in what year did the percentage of U.S. households that own a VCR reach a maximum and what was that number?

4. Do you think the model will be valid in the future for determining the percentage of U.S. households that own a VCR? Explain your thinking.

150.2t

504.6t525tP(t)

2

.8

Year % of U.S. households

that own a VCR

1980 7.24

1985 23.17

1990 35.33

1995 43.00

2000 46.78

Warm-up

where P = the percentage of U.S. households that own a VCR and t = the number of years since 1978.

ENTER THE FUNCTION IN THE Y= MENU OF YOUR GRAPHING CALCULATOR.

Use the table options on your calculator to help answer the following questions:

1. Use functional notation to represent percentage of U.S. households that owned a VCR in 1992 and determine that number. Answer to the nearest hundredth.

2. Explain what is meant by P(0), and find its value.

3. Based on the model, in what year did the percentage of U.S. households that own a VCR reach a maximum and what was that number?

4. Do you think the model will be valid in the future for determining the percentage of U.S. households that own a VCR? Explain your thinking.

150.2t

504.6t525tP(t)

2

.8

Year % of U.S. households

that own a VCR

1980 7.24

1985 23.17

1990 35.33

1995 43.00

2000 46.78

Warm-up

The percentage of U.S. households that own a VCR rose steadily since their introduction in the late 1970s. At right is a table showing the percentage of U.S. households that owned a VCR in various years (percentages rounded to the nearest hundredth).

The percentage can be modeled by the function

where P = the percentage of U.S. households that own a VCR and t = the number of years since 1978.

ENTER THE FUNCTION IN THE Y= MENU OF YOUR GRAPHING CALCULATOR.

Use the table options on your calculator to help answer the following questions:

1. Use functional notation to represent percentage of U.S. households that owned a VCR in 1992 and determine that number. Answer to the nearest hundredth.

2. Explain what is meant by P(0), and find its value.

3. Based on the model, in what year did the percentage of U.S. households that own a VCR reach a maximum and what was that number?

4. Do you think the model will be valid in the future for determining the percentage of U.S. households that own a VCR? Explain your thinking.

150.2t

504.6t525tP(t)

2

.8

Year % of U.S. households

that own a VCR

1980 7.24

1985 23.17

1990 35.33

1995 43.00

2000 46.78

The percentage of U.S. households that own a VCR rose steadily since their introduction in the late 1970s. At right is a table showing the percentage of U.S. households that owned a VCR in various years (percentages rounded to the nearest hundredth).

The percentage can be modeled by the function

where P = the percentage of U.S. households that own a VCR and t = the number of years since 1978.

ENTER THE FUNCTION IN THE Y= MENU OF YOUR GRAPHING CALCULATOR.

Use the table options on your calculator to help answer the following questions:

1. Use functional notation to represent percentage of U.S. households that owned a VCR in 1992 and determine that number. Answer to the nearest hundredth.

2. Explain what is meant by P(0), and find its value.

3. Based on the model, in what year did the percentage of U.S. households that own a VCR reach a maximum and what was that number?

4. Do you think the model will be valid in the future for determining the percentage of U.S. households that own a VCR? Explain your thinking.

150.2t

504.6t525tP(t)

2

.8

Year % of U.S. households

that own a VCR

1980 7.24

1985 23.17

1990 35.33

1995 43.00

2000 46.78

The percentage of U.S. households that own a VCR rose steadily since their introduction in the late 1970s. At right is a table showing the percentage of U.S. households that owned a VCR in various years (percentages rounded to the nearest hundredth).

The percentage can be modeled by the function

where P = the percentage of U.S. households that own a VCR and t = the number of years since 1978.

ENTER THE FUNCTION IN THE Y= MENU OF YOUR GRAPHING CALCULATOR.

Use the table options on your calculator to help answer the following questions:

1. Use functional notation to represent percentage of U.S. households that owned a VCR in 1992 and determine that number. Answer to the nearest hundredth.

2. Explain what is meant by P(0), and find its value.

3. Based on the model, in what year did the percentage of U.S. households that own a VCR reach a maximum and what was that number?

4. Do you think the model will be valid in the future for determining the percentage of U.S. households that own a VCR? Explain your thinking.

150.2t

504.6t525tP(t)

2

.8

P(14) = 38.91%

Year % of U.S. households

that own a VCR

1980 7.24

1985 23.17

1990 35.33

1995 43.00

2000 46.78

The percentage of U.S. households that own a VCR rose steadily since their introduction in the late 1970s. At right is a table showing the percentage of U.S. households that owned a VCR in various years (percentages rounded to the nearest hundredth).

The percentage can be modeled by the function

where P = the percentage of U.S. households that own a VCR and t = the number of years since 1978.

ENTER THE FUNCTION IN THE Y= MENU OF YOUR GRAPHING CALCULATOR.

Use the table options on your calculator to help answer the following questions:

1. Use functional notation to represent percentage of U.S. households that owned a VCR in 1992 and determine that number. Answer to the nearest hundredth.

2. Explain what is meant by P(0), and find its value.

3. Based on the model, in what year did the percentage of U.S. households that own a VCR reach a maximum and what was that number?

4. Do you think the model will be valid in the future for determining the percentage of U.S. households that own a VCR? Explain your thinking.

150.2t

504.6t525tP(t)

2

.8

P(14) = 38.91%

P(0) is the percentage of U.S. households that owned a VCR in 1978. P(0) = .33%

The percentage of U.S. households that own a VCR rose steadily since their introduction in the late 1970s. At right is a table showing the percentage of U.S. households that owned a VCR in various years (percentages rounded to the nearest hundredth).

The percentage can be modeled by the function

where P = the percentage of U.S. households that own a VCR and t = the number of years since 1978.

ENTER THE FUNCTION IN THE Y= MENU OF YOUR GRAPHING CALCULATOR.

Use the table options on your calculator to help answer the following questions:

1. Use functional notation to represent percentage of U.S. households that owned a VCR in 1992 and determine that number. Answer to the nearest hundredth.

2. Explain what is meant by P(0), and find its value.

3. Based on the model, in what year did the percentage of U.S. households that own a VCR reach a maximum and what was that number?

4. Do you think the model will be valid in the future for determining the percentage of U.S. households that own a VCR? Explain your thinking.

150.2t

504.6t525tP(t)

2

.8

P(14) = 38.91%

The maximum 47.87% was reached in 2005.

P(0) is the percentage of U.S. households that owned a VCR in 1978. P(0) = .33%

Answers to even-numbered HW problems

S-12

Limiting value appears to be .4

Ex 6 a) P(5) = $4,000

b)

c) The maximum profit is $7,200 (for producing 9 items)

Section 2.1

The 2 break even points are 3 items and 15 items produced.

S-8

Average Miles per Gallon (in miles per gallon) by Year of all United States Automobiles

YEAR G = Gas Mileage

1940 14.8

1950 13.2

1960 12.6

1970 13.1

1980 14.6

1986 16.0

1994 18.4

14.8.214t.0052tG(t) 2

If t represents the number of years since 1940, the function that models this data is:

0

10

20

30

40

46

54

t

Entering equations

Viewing graphs

Setting the viewing window

Tracing along a graph

14.8.214t.0052tG(t) 2

Average Miles per Gallon (in miles per gallon) by Year of all United States Automobiles

YEAR t G = Gas Mileage

1940 0 14.8

1950 10 13.2

1960 20 12.6

1970 30 13.1

1980 40 14.6

1986 46 16.0

1994 54 18.4

1. Make a graph of G versus t, where t is measured in years

since 1940.

Step 1: Enter the equation.

14.8.214t.0052tG(t) 2

1. Make a graph of G versus t, where t is measured in years

since 1940.

Step 2: Set the window using the data.

Average Miles per Gallon (in miles per gallon) by Year of all United States Automobiles

YEAR t G = Gas Mileage

1940 0 14.8

1950 10 13.2

1960 20 12.6

1970 30 13.1

1980 40 14.6

1986 46 16.0

1994 54 18.4

14.8.214t.0052tG(t) 2

1. Make a graph of G versus t, where t is measured in years

since 1940.

Step 2: Set the window using the data.

Average Miles per Gallon (in miles per gallon) by Year of all United States Automobiles

YEAR t G = Gas Mileage

1940 0 14.8

1950 10 13.2

1960 20 12.6

1970 30 13.1

1980 40 14.6

1986 46 16.0

1994 54 18.4

14.8.214t.0052tG(t) 2

1. Make a graph of G versus t, where t is measured in years

since 1940.

Step 2: Set the window using the data.

Average Miles per Gallon (in miles per gallon) by Year of all United States Automobiles

YEAR t G = Gas Mileage

1940 0 14.8

1950 10 13.2

1960 20 12.6

1970 30 13.1

1980 40 14.6

1986 46 16.0

1994 54 18.4

14.8.214t.0052tG(t) 2

1. Make a graph of G versus t, where t is measured in years

since 1940.

Step 3: View the graph.

Average Miles per Gallon (in miles per gallon) by Year of all United States Automobiles

YEAR t G = Gas Mileage

1940 0 14.8

1950 10 13.2

1960 20 12.6

1970 30 13.1

1980 40 14.6

1986 46 16.0

1994 54 18.4

14.8.214t.0052tG(t) 2

2. Use the graph to find the average gas mileage of a U.S. car in 1990.

Step 4: Press Trace and scroll to the desired year.

Average Miles per Gallon (in miles per gallon) by Year of all United States Automobiles

YEAR t G = Gas Mileage

1940 0 14.8

1950 10 13.2

1960 20 12.6

1970 30 13.1

1980 40 14.6

1986 46 16.0

1994 54 18.4

14.8.214t.0052tG(t) 2

A better way: On the graph, press Trace and type in the desired year (in this case 50) and press Enter.

Average Miles per Gallon (in miles per gallon) by Year of all United States Automobiles

YEAR t G = Gas Mileage

1940 0 14.8

1950 10 13.2

1960 20 12.6

1970 30 13.1

1980 40 14.6

1986 46 16.0

1994 54 18.4

2. Use the graph to find the average gas mileage of a U.S. car in 1990.

14.8.214t.0052tG(t) 2

3. How would you use the graph and the trace feature to find the year with the lowest (minimum) gas mileage?

Average Miles per Gallon (in miles per gallon) by Year of all United States Automobiles

YEAR t G = Gas Mileage

1940 0 14.8

1950 10 13.2

1960 20 12.6

1970 30 13.1

1980 40 14.6

1986 46 16.0

1994 54 18.4

14.8.214t.0052tG(t) 2 What if we had the function ,

where G = average gas mileage of U.S. cars and t = years since 1940

but no data table was given.

Suppose we wanted to make a graph of average gas mileage of U.S. cars from 1940 to the present.

How could we set an appropriate window for the graph?

Homework: All graphs to be done on calculator only

Read section 2.2

Page 144 # S-3, S-9, S-12

Pages 145 – 150 # 1, 4, 7, 17