Let's analyze the given expression for the company's net sales: [tex]\( t^2 + 14t + \text{constant term} \)[/tex]. We need to identify what the constant term represents in the context of the question.
Here's the detailed explanation:
1. The given expression models the net sales in billions of dollars from the year 2008 onward.
2. In the expression [tex]\( t^2 + 14t + \text{constant term} \)[/tex]:
- [tex]\( t \)[/tex] represents the number of years since 2008. For example, [tex]\( t = 0 \)[/tex] corresponds to the year 2008, [tex]\( t = 1 \)[/tex] corresponds to 2009, and so on.
3. To understand what the constant term represents, substitute [tex]\( t = 0 \)[/tex] into the expression:
[tex]\[
t^2 + 14t + \text{constant term} \rightarrow 0^2 + 14(0) + \text{constant term} = \text{constant term}
\][/tex]
4. This shows that when [tex]\( t = 0 \)[/tex], the expression simplifies to just the constant term. Therefore, the constant term represents the net sales in billions of dollars for the year 2008.
Given this information and knowing that the constant term is 85, we conclude that:
- The company earned 85 billion dollars in 2008.
Thus, the correct answer is:
- The company earned 85 billion dollars in 2008.
