tv news ratings 2-18. dependent variable given ratio independent variable

TV News Ratings

2 out of every 5 people who watch the

news, watch Channel 11 News @ 6:00.

# of people who watch the Channel 11 News @ 6:00 2

# of people who watch the news 5

Let The # of people who watch the Channel 11 News @ 6:00N Let The total # of people who watch the newsT

2

5

2

5

NT NTT

T

11

2-18

1. Approximately how many people watch Channel 11,

if the total number of people who watch the news is:

(a) 10 people

(b) 1,000 people

(c) 10,000 people

In a complete sentence, explain how you found these answers.

4400

4000

2

5N T

The number of people who watch the Channel

11 News @ 6:00 is two-fifths times the total number

of people who watch the news.

N

T

Let The # of people who watch the Channel 11 News @ 6:00N Let The total # of people who watch the newsT

:Verbal Model

The number of people

who watch the Channel

11 News @ 6:00

N

2

5 The total number of people

who watch the news

T

The number of people who watch the Channel

11 News @ 6:00 is two-fifths times the total number

of people who watch the news.

N

T

Algebraic Model:

2

5N TDependent

Variable

Given Ratio

Independent Variable

2. Approximately how many people watch any news,

if the number of people who watch Channel 11 news is:

(a) 20 people

(b) 200 people

(c) 20,000 people

In a complete sentence, explain how you found these answers.

50500

50,000

5 5 2

2 2 5N T

5

2T N

The total number of people who watch the news

is five-halves of the number of people who

watch the Channel 11 News @ 6:00.

T

N

Let The # of people who watch the Channel 11 News @ 6:00N Let The total # of people who watch the newsT

:Verbal Model

The number of people

who watch the Channel

11 News @ 6:00

N

5

2 The total number of people

who watch the news

T

Algebraic Model:

5

2T NDependent

Variable

New Ratio

Independent Variable

The total number of people who watch the news

is five-halves of the number of people who

watch the Channel 11 News @ 6:00.

T

N

3. Let represent the total number of people who watch

any news at 6:00. Write an equation for , the number of

people who watch the Channel 11 News at 6:00.

T

N

2

5N T

4. Use the information you have developed so far

to clearly redefine the problem situation.

TV News RatingsTV News Ratings

#8

2

5N T

The number of people

who watch the Channel

11 News @ 6:00

N

2

5 The total number of people

who watch the news

T

Graph

5. Create a table of values for this situation

and include the expression.

Total number of people who watch the news at 6:00

The number of people who watch the Channel 11 News at 6:00

People People

T 2/5*T

1000 400

10,000 4000

100,000 40,000

150,000 60,000

300,000 120,000

Labels

Units

Expression

6. Plot the points from the data table, making sure to label your axes

appropriately and using an appropriate scale for each axis.

T 0 500,000 25,000

N=2/5T 0 150,000 10,000

Variable Quantity Lower Bound Upper Bound Interval

Total # of people who watch the news at 6:00 (T)# w

ho w

atch

the

Cha

nnel

11

New

s at

6:0

0

(

N)

25k

10kTable

#7

#9

7. What are the variable quantities in the problem situation?

Include the units that measure these quantities.

TV News Ratings

Total # of people who watch the news at 6:00 (T)

# of people who watch the Channel 11 News at 6:00 (N)

Graph

11

8. What is the common ratio in the problem situation?

TV News Ratings

Graph

Verbal Model

2

5

11

9. Of the two variable quantities, which quantity depends

on the other quantity?

TV News Ratings

Graph

Verbal Model

# who watch the Channel 11 News at 6:00 (N)

depends on

Total # of people who watch the news at 6:00 (T)

11

10. What is the independent variable quantity, and what

is the dependent quantity in the problem situation?

TV News Ratings

Graph

Verbal Model

# who watch the Channel 11 News at 6:00 (N)

depends on

Total # of people who watch the news at 6:00 (T)

Dependent

Independent

11

11. The producers of a competing news show on Channel 4

tell the commercial sponsors that their 6:00 News has one

of every three viewers watching it. Should the advertisers

place their commercial on Channel 11 or Channel 4 if they

want to reach the largest television viewing audience?

Explain your reasoning.

TV News Ratings

Channel 4

10.3 33%

3

N

T

Channel 11 20.4 40%

5

N

T

4