Certainly! To determine the number of customers in month 20 using the given model [tex]\( y = 10x^2 + 50x + 300 \)[/tex], follow these steps:
1. Identify the value of [tex]\( x \)[/tex] for which we need to find the number of customers. In this case, [tex]\( x = 20 \)[/tex] (since we are interested in month 20).
2. Substitute [tex]\( x = 20 \)[/tex] into the equation [tex]\( y = 10x^2 + 50x + 300 \)[/tex].
3. Calculate the value of [tex]\( y \)[/tex] by evaluating the expression step-by-step.
Let's break it down:
- Start with the given equation:
[tex]\[
y = 10x^2 + 50x + 300
\][/tex]
- Substitute [tex]\( x = 20 \)[/tex] into the equation:
[tex]\[
y = 10(20)^2 + 50(20) + 300
\][/tex]
- Calculate [tex]\( (20)^2 \)[/tex]:
[tex]\[
(20)^2 = 400
\][/tex]
- Multiply this result by 10:
[tex]\[
10 \cdot 400 = 4000
\][/tex]
- Next, multiply [tex]\( 50 \)[/tex] by [tex]\( 20 \)[/tex]:
[tex]\[
50 \cdot 20 = 1000
\][/tex]
- Now add all the obtained values together:
[tex]\[
y = 4000 + 1000 + 300
\][/tex]
- Finally, sum all the terms:
[tex]\[
y = 5300
\][/tex]
Therefore, the best prediction for the number of customers in month 20 is:
D. 5300
