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Select the correct answer.

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 2011, 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 2006, 44,500 units are produced.

Answer :

To solve the problem and interpret the meaning of [tex]\( f(6) = 44,500 \)[/tex], we need to consider what each part of this notation represents. Here's a detailed, step-by-step explanation:

1. Understanding the Function Notation:
- The function [tex]\( f(t) \)[/tex] represents the number of units produced by a company [tex]\( t \)[/tex] years after it opened.

2. Identifying the Start Year:
- The company opened in 2005.

3. Analyzing the Given Expression [tex]\( f(6) = 44,500 \)[/tex]:
- The notation [tex]\( f(6) \)[/tex] indicates that we are looking at the number of units produced 6 years after the company opened.

4. Calculating the Year:
- Since the company opened in 2005, and we are interested in production 6 years after opening:
- Add the 6 years to the opening year:
[tex]\[ 2005 + 6 = 2011 \][/tex]
- So, 6 years after the company opened is the year 2011.

5. Interpreting the Statement [tex]\( f(6) = 44,500 \)[/tex]:
- The number [tex]\( 44,500 \)[/tex] represents the units produced in that particular year.
- Therefore, in the year 2011, the company produced 44,500 units.

In conclusion, the correct interpretation of [tex]\( f(6) = 44,500 \)[/tex] is: "In 2011, 44,500 units are produced."