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Answer :
To solve this problem, we need to interpret the meaning of [tex]\( f(6) = 44,500 \)[/tex] for the function [tex]\( f(t) \)[/tex], which represents the number of units produced by the company [tex]\( t \)[/tex] years after opening in 2005.
Let's analyze this step-by-step:
1. Understanding the Function: The function [tex]\( f(t) \)[/tex] tells us the number of units produced [tex]\( t \)[/tex] years after the company started in 2005.
2. Finding the Year: The expression [tex]\( f(6) = 44,500 \)[/tex] tells us that the function [tex]\( f \)[/tex] evaluates to 44,500 when [tex]\( t = 6 \)[/tex]. This means 6 years after the company started, 44,500 units were produced.
3. Calculating the Year: Since the company started in 2005, we add the 6 years to 2005 to find the specific year when 44,500 units were produced:
[tex]\[
2005 + 6 = 2011
\][/tex]
4. Conclusion: Therefore, in the year 2011, the company produced 44,500 units.
The correct interpretation of [tex]\( f(6) = 44,500 \)[/tex] is that in 2011, 44,500 units were produced. This matches with the answer option: "In 2011, 44,500 units are produced."
Let's analyze this step-by-step:
1. Understanding the Function: The function [tex]\( f(t) \)[/tex] tells us the number of units produced [tex]\( t \)[/tex] years after the company started in 2005.
2. Finding the Year: The expression [tex]\( f(6) = 44,500 \)[/tex] tells us that the function [tex]\( f \)[/tex] evaluates to 44,500 when [tex]\( t = 6 \)[/tex]. This means 6 years after the company started, 44,500 units were produced.
3. Calculating the Year: Since the company started in 2005, we add the 6 years to 2005 to find the specific year when 44,500 units were produced:
[tex]\[
2005 + 6 = 2011
\][/tex]
4. Conclusion: Therefore, in the year 2011, the company produced 44,500 units.
The correct interpretation of [tex]\( f(6) = 44,500 \)[/tex] is that in 2011, 44,500 units were produced. This matches with the answer option: "In 2011, 44,500 units are produced."
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