Question 1102124: The number of inmates N (measured in thousands) in federal and state prisons can be approximated by the equation N = -2.05x squared + 77.85x + 746, where x is the number of years since 1990. In what year was the number of inmates expected to be 1,280,600? THANK YOU!!!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
N is the number of inmates in thousands. If we wrote N = 2, then that means we have 2000 inmates. Going from 2 to 2000 has us multiply by 1000.
Going in reverse, having 1,280,600 inmates means that N = 1280.6 (divide 1,280,600 by 1000; or move the decimal point 3 spots to the left)
So we need to plug in N = 1280.6 and then solve for x
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N = -2.05x^2+77.85x+746
1280.6 = -2.05x^2+77.85x+746 replace N with 1280.6
1280.6-1280.6 = -2.05x^2+77.85x+746-1280.6 Subtract 1280.6 from both sides
0 = -2.05x^2+77.85x-534.6
-2.05x^2+77.85x-534.6 = 0
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The equation -2.05x^2+77.85x-534.6 = 0 is in the form ax^2+bx+c = 0, where,
a = -2.05
b = 77.85
c = -534.6
Use the quadratic formula to solve. Plug those a,b,c values into the formulas below and simplify
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The two solutions are or
If you want x to be a whole number, then ignore the second solution. In this case, it will take exactly 9 years from 1990 for the inmate population to be at 1,280,600. So this happens in the year 1990+9 = 1999
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