To determine the number of prisoners held in federal and state prisons in the year 1990, we need to evaluate the polynomial [tex]\( -2.03x^2 + 78.07x + 747 \)[/tex] at [tex]\( x = 0 \)[/tex], where [tex]\( x \)[/tex] represents the number of years since 1990.
Since 1990 is our baseline year, [tex]\( x = 0 \)[/tex]. Substituting [tex]\( x = 0 \)[/tex] into the polynomial, we get:
[tex]\[ -2.03(0)^2 + 78.07(0) + 747 \][/tex]
Simplifying the expression step-by-step:
1. Compute [tex]\( (0)^2 \)[/tex]:
[tex]\[ (0)^2 = 0 \][/tex]
2. Multiply by the coefficient [tex]\(-2.03\)[/tex]:
[tex]\[ -2.03 \times 0 = 0 \][/tex]
3. Multiply [tex]\( 78.07 \times 0 \)[/tex]:
[tex]\[ 78.07 \times 0 = 0 \][/tex]
4. Add the constant term [tex]\( 747 \)[/tex]:
[tex]\[ 0 + 0 + 747 = 747 \][/tex]
Therefore, the number of prisoners in federal and state prisons in the year 1990 was [tex]\( 747 \)[/tex] thousand.
So, the prison population in 1990 was [tex]\( \boxed{747} \)[/tex] thousand.
