hello my name is patricia

Question

number of inmates in federal prison can be approximated by the equation N=-2.01x²+77.86x+749, where x is the number of years since 1990. in what year was the number of inmates expected to be 1,195,530?

Answer 1

The problem gives a quadratic formula to model N, the number of inmates, given x, the number of years since 1990.

 

We may either (1) use N=1195530 in the formula and solve for x, or we may (2) calculate values of N for x until we find the correct value of x.  Let's put the formula into a spreadsheet:

 

year    x           N/1000

1990   0         749.00
1991   1         824.85
1992   2         896.68
1993   3         964.49
1994   4       1028.28
1995   5       1088.05
1996   6       1143.80
1997  7       1195.53
1998   8       1243.24
1999   9       1286.93

 

Now, we must assume that N is in thousands.  1195.53 and x=7 occur when Year = 1997.