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

Answer :

We are given that the function [tex]\( f(t) \)[/tex] represents the number of units produced [tex]\( t \)[/tex] years after the company opened in 2005. When we evaluate the function at [tex]\( t = 6 \)[/tex], we have:

[tex]$$
f(6) = 44500.
$$[/tex]

Here, [tex]\( t = 6 \)[/tex] corresponds to 6 years after the opening year of 2005. To determine the actual production year, we calculate:

[tex]$$
\text{Year of production} = 2005 + 6 = 2011.
$$[/tex]

Thus, [tex]\( f(6) = 44500 \)[/tex] means that in the year 2011, the company produced 44,500 units.

The correct interpretation is:

In 2011, 44,500 units are produced.

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