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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 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 the company [tex]\( t \)[/tex] years after it opened in 2005. This means that when [tex]\( t = 0 \)[/tex], the year is 2005, when [tex]\( t = 1 \)[/tex], the year is 2006, and so on.

1. For [tex]\( t = 6 \)[/tex], the corresponding year is calculated by adding 6 years to 2005:
[tex]$$
2005 + 6 = 2011.
$$[/tex]

2. The statement [tex]\( f(6) = 44,\!500 \)[/tex] tells us that in the year 2011, the company produced 44,500 units.

Thus, the correct interpretation of [tex]\( f(6)=44,\!500 \)[/tex] is:

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

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