To determine the best prediction for the amount Eric will have saved after 20 months, we'll utilize the regression equation provided:
[tex]\[ y = 8x^2 + 100x + 250 \][/tex]
Here, [tex]\( x \)[/tex] represents the number of months, which is 20 in this case.
Let's substitute [tex]\( x = 20 \)[/tex] into the equation to find [tex]\( y \)[/tex]:
1. Substitute [tex]\( x \)[/tex] into the equation:
[tex]\[ y = 8(20)^2 + 100(20) + 250 \][/tex]
2. Calculate [tex]\( (20)^2 \)[/tex]:
[tex]\[ 20^2 = 400 \][/tex]
3. Multiply by the coefficient 8:
[tex]\[ 8 \times 400 = 3200 \][/tex]
4. Multiply 100 by 20:
[tex]\[ 100 \times 20 = 2000 \][/tex]
5. Add up all the terms:
[tex]\[ y = 3200 + 2000 + 250 = 5450 \][/tex]
Thus, the best prediction for the amount Eric will have saved after 20 months is:
[tex]\[ y = \$5450 \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{5450} \][/tex]
