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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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