Answered

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The number of customers for a new online business can be modeled by [tex]$y = 8x^2 + 100x + 250[tex]$[/tex], where [tex]$[/tex]x$[/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. 5450
C. 3550
D. 7750

Sagot :

GinnyAnswer
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]
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