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The number of customers for a new online business can be modeled by [tex]\( y = 8x^2 + 100x + 250 \)[/tex], where [tex]\( x \)[/tex] represents the number of months since the business started.

Which is the best prediction for the number of customers in month 20?

A. 2050
B. 3550
C. 7750
D. 5450

Sagot :

GinnyAnsweridn
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
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