Answer :
To determine the number of customers for the new online business in month 20, we start with the given quadratic function:
[tex]\[ y = 8x^2 + 100x + 250 \][/tex]
Here, \( x \) represents the number of months since the business started. Thus, for month 20, we need to substitute \( x = 20 \) into the equation.
[tex]\[ y = 8(20)^2 + 100(20) + 250 \][/tex]
First, calculate \( 20^2 \):
[tex]\[ 20^2 = 400 \][/tex]
Next, multiply this result by 8:
[tex]\[ 8 \times 400 = 3200 \][/tex]
Then, calculate \( 100 \times 20 \):
[tex]\[ 100 \times 20 = 2000 \][/tex]
Now, sum these two results along with the constant 250:
[tex]\[ 3200 + 2000 + 250 = 5450 \][/tex]
Therefore, the number of customers in month 20 is:
[tex]\[ \boxed{5450} \][/tex]
So, the best prediction for the number of customers in month 20 is:
[tex]\[ \text{B. 5450} \][/tex]
[tex]\[ y = 8x^2 + 100x + 250 \][/tex]
Here, \( x \) represents the number of months since the business started. Thus, for month 20, we need to substitute \( x = 20 \) into the equation.
[tex]\[ y = 8(20)^2 + 100(20) + 250 \][/tex]
First, calculate \( 20^2 \):
[tex]\[ 20^2 = 400 \][/tex]
Next, multiply this result by 8:
[tex]\[ 8 \times 400 = 3200 \][/tex]
Then, calculate \( 100 \times 20 \):
[tex]\[ 100 \times 20 = 2000 \][/tex]
Now, sum these two results along with the constant 250:
[tex]\[ 3200 + 2000 + 250 = 5450 \][/tex]
Therefore, the number of customers in month 20 is:
[tex]\[ \boxed{5450} \][/tex]
So, the best prediction for the number of customers in month 20 is:
[tex]\[ \text{B. 5450} \][/tex]
