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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 :

We are given that the function [tex]\( f(t) \)[/tex] represents the number of units produced by a company [tex]\( t \)[/tex] years after it opened in 2005. The equation

[tex]$$
f(6) = 44,\!500
$$[/tex]

indicates that 6 years after the company opened, the production was 44,500 units.

Since the company opened in 2005, we add 6 years to get the corresponding year:

[tex]$$
2005 + 6 = 2011.
$$[/tex]

Therefore, the interpretation of [tex]\( f(6) = 44,\!500 \)[/tex] is that in 2011, 44,500 units were produced.

Thus, the correct choice is:

[tex]$$
\text{In 2011, 44,500 units are produced.}
$$[/tex]

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