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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 2006, 44,500 units are produced.

B. Six years from now, 44,500 units will be produced.

C. In 2011, 44,500 units are produced.

D. In 2009, 44,500 units are produced.

Answer :

To solve this problem, we need to understand what the function [tex]\( f(t) \)[/tex] represents. The function [tex]\( f(t) \)[/tex] gives the number of units produced by a company [tex]\( t \)[/tex] years after the year 2005.

Given the information [tex]\( f(6) = 44,500 \)[/tex], this tells us that 44,500 units were produced when [tex]\( t = 6 \)[/tex].

Now, we need to interpret what year [tex]\( t = 6 \)[/tex] corresponds to:

1. Start year: The company began production in the year 2005.
2. Calculate the year for [tex]\( t = 6 \)[/tex]:
- Since [tex]\( t \)[/tex] represents the number of years after 2005, we add 6 years to 2005.
- [tex]\( 2005 + 6 = 2011 \)[/tex].

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

"In 2011, 44,500 units are produced."

This matches the option stating that in 2011, the company produced 44,500 units.

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