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

Year

State B

State A

10.0

2002

6.9

2003

9.6

2004

9.2

6.3

6.0

5.6

2005

8.8

(a) What variables are appropriate?

t(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)

ot(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)

ot(years since 2000)

A (the percentage of teenagers in State A)

B (the percentage of teenagers in State B)

O

(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)

-2.5x + 2027

=

(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.

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.

O

(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)

-.43b – .01 x

=

(e) Estimate when the percentage of births to teenage mothers in State B was greater than the percentage in State A.

Before

the percentage of births to teenage mothers in State B was greater than the number in State A.

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

y

f(x)

4

3

NO

х

4

-2

2

6

8

Solve the inequality, writing the solution in interval notation.

If you need to signify use -INF or use INF.

24 < 2x + 12 < 62
6
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