Poverty Level From 2005 through 2013, the population p (in millions) living below poverty in the United States can be modeled by p = 0.01469 t 4 − 0.6364 t 3 + 9.677 t 2 − 59.63 t + 163.8 for 5 ≤ t ≤ 13 , where t is the year, with t = 5 corresponding to 2005. (Source: U.S. Census Bureau) (a) Use a graphing utility to graph the model on the interval [ 5 , 13 ] . (b) Use the second derivative to determine the concavity of the graph of p. (c) Find the point(s) of inflection of the graph of p. (d) Interpret the meaning of the point(s) of inflection from part (c). Freshii
Poverty Level From 2005 through 2013, the population p (in millions) living below poverty in the United States can be modeled by p = 0.01469 t 4 − 0.6364 t 3 + 9.677 t 2 − 59.63 t + 163.8 for 5 ≤ t ≤ 13 , where t is the year, with t = 5 corresponding to 2005. (Source: U.S. Census Bureau) (a) Use a graphing utility to graph the model on the interval [ 5 , 13 ] . (b) Use the second derivative to determine the concavity of the graph of p. (c) Find the point(s) of inflection of the graph of p. (d) Interpret the meaning of the point(s) of inflection from part (c). Freshii
Solution Summary: The author explains how to draw the graph in a graphing utility like TI-83.
Poverty Level From 2005 through 2013, the population p (in millions) living below poverty in the United States can be modeled by
p
=
0.01469
t
4
−
0.6364
t
3
+
9.677
t
2
−
59.63
t
+
163.8
for
5
≤
t
≤
13
, where t is the year, with
t
=
5
corresponding to 2005. (Source: U.S. Census Bureau)
(a) Use a graphing utility to graph the model on the interval
[
5
,
13
]
.
(b) Use the second derivative to determine the concavity of the graph of p.
(c) Find the point(s) of inflection of the graph of p.
(d) Interpret the meaning of the point(s) of inflection from part (c).
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