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

Answer :

To interpret the statement [tex]\( f(6) = 44,500 \)[/tex], we need to understand what each part of the notation means:

1. The function [tex]\( f(t) \)[/tex] represents the number of units produced by the company [tex]\( t \)[/tex] years after the company opened in 2005.

2. The notation [tex]\( f(6) = 44,500 \)[/tex] tells us that when [tex]\( t = 6 \)[/tex], the function [tex]\( f(t) \)[/tex] equals 44,500. This means that 44,500 units were produced at that particular point in time.

3. To find out which year corresponds to [tex]\( t = 6 \)[/tex], add 6 years to the starting year, which is 2005:
[tex]\[
2005 + 6 = 2011
\][/tex]

Putting this together, it means that in the year 2011, the company produced 44,500 units.

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