The number of prisoners measured in thousands can be described by the polynomial -2.06x^2+77.85x+750. According to the polynomial, by how much did the prison population increase from 2002 to 2007?
The question only makes sense if we know the definition of x.
Is x the number of years since 2000?
Thanks I figured it out. The definition of x is the numbers since 1990.
To find the increase in the prison population from 2002 to 2007, you need to subtract the value of the polynomial at 2002 from the value of the polynomial at 2007.
The given polynomial is -2.06x^2 + 77.85x + 750, where 'x' represents the number of years after 2000.
To find the prison population in 2002, substitute x = 2 into the polynomial:
P(2) = -2.06(2)^2 + 77.85(2) + 750
P(2) = -2.06(4) + 155.7 + 750
P(2) = -8.24 + 155.7 + 750
P(2) = 897.46
So, the prison population in 2002, measured in thousands, is 897.46 thousand.
Now, let's find the prison population in 2007. Substitute x = 7 into the polynomial:
P(7) = -2.06(7)^2 + 77.85(7) + 750
P(7) = -2.06(49) + 544.95 + 750
P(7) = -100.94 + 544.95 + 750
P(7) = 1194.01
So, the prison population in 2007, measured in thousands, is 1194.01 thousand.
To find the increase in the prison population from 2002 to 2007, subtract the population in 2002 from the population in 2007:
Increase = P(2007) - P(2002)
Increase = 1194.01 - 897.46
Increase = 296.55
Therefore, according to the given polynomial, the prison population increased by 296.55 thousand from 2002 to 2007.