To determine the best prediction for the number of customers in month 20, we can use the given equation:
[tex]\[ y = 8x^2 + 100x + 250 \][/tex]
Here, [tex]\( x \)[/tex] represents the number of months since the business started. We need to find the number of customers when [tex]\( x = 20 \)[/tex].
Step-by-step solution:
1. Substitute [tex]\( x = 20 \)[/tex] into the equation:
[tex]\[ y = 8(20)^2 + 100(20) + 250 \][/tex]
2. Calculate the square of 20:
[tex]\[ 20^2 = 400 \][/tex]
3. Multiply 8 by the square of 20:
[tex]\[ 8 \times 400 = 3200 \][/tex]
4. Multiply 100 by 20:
[tex]\[ 100 \times 20 = 2000 \][/tex]
5. Add these values together along with the constant term 250:
[tex]\[ y = 3200 + 2000 + 250 \][/tex]
[tex]\[ y = 5450 \][/tex]
Therefore, the best prediction for the number of customers in month 20 is [tex]\( 5450 \)[/tex].
The correct answer is:
D. 5450
