Question

From 2000 to 2009 the annual sales S (in millions of dollars) of a certain company can be modeled by where t is the number of years since 2000.

a) Approximate the year in which sales reached a low point for the company.
A) 2005
B) 2006
C) 2007
D) 2008

b) If the polynomial function continues to model the sales of the company in the future, what can the expected sales be in 2015?
A) $1.2 million
B) $2.3 million
C) $2.8 million
D) $3.5 million

Answer 1

To predict sales using the given linear regression model, multiply the day number by 2.48 and add to 101.32. Predicted sales are $250.12 thousand for day 60 and $324.52 thousand for day 90.

Step-by-step explanation:

The student's question is related to finding the low point in the sales of a company from the year 2000 to 2009 and predicting future sales using a polynomial function. Without the actual polynomial function provided, it's impossible to definitively answer part a). However, for answering part b) of the question about sales prediction for 2015 using a polynomial function, we would need the actual polynomial expression to perform the prediction. Instead, we can answer a similar type of question using the linear regression model û = 101.32 + 2.48x, where x is the day and û is the predicted sales in thousands of dollars.

For day 60, the predicted sales would be û = 101.32 + 2.48(60) = 101.32 + 148.8 = $250.12 thousand.

For day 90, the predicted sales would be û = 101.32 + 2.48(90) = 101.32 + 223.2 = $324.52 thousand.