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Answer :
To correctly interpret the statement [tex]\( f(6) = 44,500 \)[/tex], follow these steps:
1. Understand the function [tex]\( f(t) \)[/tex]:
- The function [tex]\( f(t) \)[/tex] represents the number of units produced by a company [tex]\( t \)[/tex] years after it opened in 2005.
2. Identify what [tex]\( t = 6 \)[/tex] means:
- Since [tex]\( t \)[/tex] represents years after 2005, if [tex]\( t = 6 \)[/tex], this means 6 years after the company started in 2005.
3. Calculate the corresponding year:
- Start from the year the company opened: 2005.
- Add the 6 years to 2005: [tex]\( 2005 + 6 = 2011 \)[/tex].
4. Interpret the value [tex]\( f(6) = 44,500 \)[/tex]:
- The value [tex]\( 44,500 \)[/tex] corresponds to the number of units produced by the company at [tex]\( t = 6 \)[/tex] years after opening.
- Based on the calculation, [tex]\( t = 6 \)[/tex] corresponds to the year 2011.
Therefore, the correct interpretation of [tex]\( f(6) = 44,500 \)[/tex] is:
In 2011, 44,500 units are produced.
1. Understand the function [tex]\( f(t) \)[/tex]:
- The function [tex]\( f(t) \)[/tex] represents the number of units produced by a company [tex]\( t \)[/tex] years after it opened in 2005.
2. Identify what [tex]\( t = 6 \)[/tex] means:
- Since [tex]\( t \)[/tex] represents years after 2005, if [tex]\( t = 6 \)[/tex], this means 6 years after the company started in 2005.
3. Calculate the corresponding year:
- Start from the year the company opened: 2005.
- Add the 6 years to 2005: [tex]\( 2005 + 6 = 2011 \)[/tex].
4. Interpret the value [tex]\( f(6) = 44,500 \)[/tex]:
- The value [tex]\( 44,500 \)[/tex] corresponds to the number of units produced by the company at [tex]\( t = 6 \)[/tex] years after opening.
- Based on the calculation, [tex]\( t = 6 \)[/tex] corresponds to the year 2011.
Therefore, the correct interpretation of [tex]\( f(6) = 44,500 \)[/tex] is:
In 2011, 44,500 units are produced.
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