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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 Purchase answer to see full attachment

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