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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 2009, 44,500 units are produced.
B. In 2006, 44,500 units are produced.
C. In 2011, 44,500 units are produced.
D. Six years from now, 44,500 units will be produced.

Answer :

To interpret the statement [tex]\( f(6) = 44,500 \)[/tex], let's break down what it means. The function [tex]\( f(t) \)[/tex] represents the number of units produced [tex]\( t \)[/tex] years after the company opened. Since the company started in 2005, the variable [tex]\( t \)[/tex] shows how many years have passed since then.

1. The statement [tex]\( f(6) = 44,500 \)[/tex] tells us that when [tex]\( t = 6 \)[/tex], the number of units produced is 44,500.
2. Now, let’s determine the year associated with [tex]\( t = 6 \)[/tex].
3. Since the company opened in 2005, we calculate the year by adding 6 to 2005:

[tex]\[
2005 + 6 = 2011
\][/tex]

So, the correct interpretation of [tex]\( f(6) = 44,500 \)[/tex] is that in the year 2011, the company produced 44,500 units.

Thus, the correct answer is:

In 2011, 44,500 units are produced.

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