The number of customers for a new online business can be modeled by y= 10x² + 50x + 300, where x represents the number of months since the business started. Which is the best prediction for the number of customers in month 20?
A. 9540
B. 10,800
C. 7260
D. 5300
Answer (2)
Substitute x = 20 into the equation y = 10 x 2 + 50 x + 300 .
Calculate y = 10 ( 20 ) 2 + 50 ( 20 ) + 300 .
Simplify the equation to find y = 4000 + 1000 + 300 .
The predicted number of customers in month 20 is 5300 .
Explanation
Understanding the Problem We are given the equation y = 10 x 2 + 50 x + 300 that models the number of customers for a new online business, where x is the number of months since the business started. We want to find the best prediction for the number of customers in month 20.
Substituting x = 20 To find the predicted number of customers in month 20, we substitute x = 20 into the equation: y = 10 ( 20 ) 2 + 50 ( 20 ) + 300
Calculating y Now, we calculate the value of y :
y = 10 ( 400 ) + 1000 + 300 y = 4000 + 1000 + 300 y = 5300
Final Answer Therefore, the best prediction for the number of customers in month 20 is 5300.
Examples
Imagine you are starting your own lemonade stand. The equation provided helps you predict how many customers you might have each month based on your initial growth. By understanding and using this equation, you can plan how much lemonade to make, how many cups to buy, and how many helpers you might need. This kind of prediction is useful for managing resources and making sure you're prepared for the future success of your business.
By substituting x = 20 into the equation y = 10 x 2 + 50 x + 300 , we calculate the predicted number of customers to be 5300. Therefore, the best answer is 5300 customers.
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