Shawn S.

asked • 07/08/16

what year 9

The number of inmates N? (measured in? thousands) in federal and state prisons can be approximated by the equation N=−2.05x2+77.82x+747?,
where x is the number of years since 1990. In what year was the number of inmates expected to be 1,281,330??

1 Expert Answer

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Michael J. answered • 07/08/16

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Since N is represented in thousands,
 
N = 1.281330 × 106
 
N = 1281.330 × 103
 
N = 1281.330
 
 
What you will do is solve for x when N=1281.330, using the quadratic formula:
 
x = (-b ± √(b2 - 4ac)) / 2a
 
where:
a = -2.05
b = 77.82
c = 747
 
Plug in these values into the formula.  Be sure to chose the positive value of x and round to the nearest integer.  Then you will add 1990 to the x value.
 
 
Solution:
Year = 1990 + x
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Shawn S.

Im not seeing an answer to compare to
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07/08/16

Michael J.

If you follow my steps, then you will have a the correct answer.  If you are looking to compare an answer to a textbook, then there is a good chance the book is wrong.
 
What answer did you get when you worked it out?
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07/08/16

David W.

Here are some values to compare with your answer:
 
Year        x           N
1990       0         747
1991       1        822.77
1992       2       894.44
1993       3       962.01
1994       4     1025.48
1995       5     1084.85
1996       6     1140.12
1997       7     1191.29
1998       8     1238.36
1999       9     1281.33
2000     10     1320.2
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07/08/16

David W.

Just to note:  Normally, algebra teaches you to use the straight-forward method of "working it out" using the quadratic formula.  What is often missing in that approach is estimating, guessing (even intelligent guessing), and solving for N using all values of x (for example, using a spreadsheet program on a computer).  Someday, you will have the choice of using the method that works best for you.
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07/08/16

Michael J.

As long common core exists, students will never have a method of choice.  The curriculum requires them to learn concepts a certain way.  If one tries to answer a question their own way on a common core test, it is likely one will lose points.
 
Guessing is a great approach to learning the process, but time is scarce when taking tests.  This is the part where students may want to use a method they are more comfortable with and less time consuming.
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07/08/16

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