Use the graph to find when f(x) = g(x).

x

y

f(x)

4

3

2

х

4

-2

2

6

8

The percentages of births to teenage mothers in the United States for two states are given below.

Year

State A

State B

2002

10.0

6.9

2003

9.6

6.3

2004

9.2

6.0

2005

8.8

5.6

(a) What variables are appropriate?

ot(years since 2000)

A (the number of births to teenage mothers in State A)

B (the number of births to teenage mothers in State B)

ot(years since 2000)

A (the number of births to mothers in State A)

B (the number of births to mothers in State B)

o t (years since 2000)

A (the percentage of births to mothers in State A)

B (the percentage of births to mothers in State B)

t(years since 2000)

A (the percentage of births to teenage mothers in State A)

B (the percentage of births to teenage mothers in State B)

t (years since 2000)

A (the percentage of teenagers in State A)

B (the percentage of teenagers in State B)

(b) Find a model for the percentage of births to teenage mothers in State A. (Use the first and last values in the table to calculate your equation.)

A(t)

..4t + 810.8 x

(c) What does the slope for the model in part (b) mean in this context?

The slope is 10.8 which means that the percent of births to teenage mothers in State A is increasing by 10.8 percent per year.

The slope is 10.8 which means that the percent of births to teenage mothers in State A is decreasing by 10.8 percent per year.

o The slope is -0.4 which means that the percent of births to teenage mothers in State A is increasing by 0.4 percent per year.

• The slope -0.4 which means that the percent of births to teenage mothers is State A is decreasing by 0.4 percent per year.

(d) Find a model for the percentage of births to teenage mothers in State B. (Use the first and third values in the table to calculate your equation.)

B(t)

=

-0.45t + 907.8 x

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