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Let [tex]f(t)[/tex] be the number of units produced by a company [tex]t[/tex] years after opening in 2005. What is the correct interpretation of [tex]f(6) = 44,500[/tex]?

A. In 2006, 44,500 units are produced.
B. In 2009, 44,500 units are produced.
C. Six years from now, 44,500 units will be produced.
D. In 2011, 44,500 units are produced.

Answer :

To interpret the expression [tex]\( f(t) = 44,500 \)[/tex] where [tex]\( t \)[/tex] represents the years after the company opened in 2005, let's carefully break this down step-by-step:

1. Understanding the function [tex]\( f(t) \)[/tex]:
- [tex]\( f(t) \)[/tex] is the number of units produced [tex]\( t \)[/tex] years after the company opened.

2. Identify the starting year of the company:
- The company opened in 2005.

3. Analyze the given value [tex]\( f(6) = 44,500 \)[/tex]:
- This means [tex]\( t = 6 \)[/tex] years after the company opened.

4. Calculate the corresponding year:
- To find the year corresponding to [tex]\( t = 6 \)[/tex], add 6 years to 2005:
[tex]\[
2005 + 6 = 2011
\][/tex]

5. Interpret the value [tex]\( 44,500 \)[/tex]:
- According to [tex]\( f(6) = 44,500 \)[/tex], 44,500 units were produced 6 years after the company opened.

Putting all of this together, we interpret [tex]\( f(6) = 44,500 \)[/tex] to mean that in the year 2011, 44,500 units were produced.

Thus, the correct interpretation is:
In 2011, 44,500 units are produced.

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