Prison Population The number of prisoners in state prisons in the United States can be approximated by N ( x , y ) = − 540 + 7.5 x + 2.5 y − 0.01 x y thousand inmates, where x is the number, in thousands, in federal prisons and y is the number, in thousands, in local jails. 7 a. In 2010 there were approximately 198 thousand prisoners in federal prisons and 749 thousand in local jails. Estimate, to the nearest 0.1 million, the number of prisoners in state prisons that year. b. Obtain N as a function of y for x = 80 and again for x = 100 . Interpret the slopes of the resulting linear functions.
Prison Population The number of prisoners in state prisons in the United States can be approximated by N ( x , y ) = − 540 + 7.5 x + 2.5 y − 0.01 x y thousand inmates, where x is the number, in thousands, in federal prisons and y is the number, in thousands, in local jails. 7 a. In 2010 there were approximately 198 thousand prisoners in federal prisons and 749 thousand in local jails. Estimate, to the nearest 0.1 million, the number of prisoners in state prisons that year. b. Obtain N as a function of y for x = 80 and again for x = 100 . Interpret the slopes of the resulting linear functions.
Solution Summary: The author calculates the number of prisoners in federal prisons in the United States, based on 198 and 749 in local jails.
Prison Population The number of prisoners in state prisons in the United States can be approximated by
N
(
x
,
y
)
=
−
540
+
7.5
x
+
2.5
y
−
0.01
x
y
thousand inmates, where x is the number, in thousands, in federal prisons and y is the number, in thousands, in local jails.7
a. In 2010 there were approximately 198 thousand prisoners in federal prisons and 749 thousand in local jails. Estimate, to the nearest 0.1 million, the number of prisoners in state prisons that year.
b. Obtain N as a function of y for
x
=
80
and again for
x
=
100
. Interpret the slopes of the resulting linear functions.
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