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Answer :
To interpret [tex]\( f(6) = 44,500 \)[/tex], we need to understand what the given information means in the context of the problem. Here’s a step-by-step breakdown:
1. Understand the function notation: The function [tex]\( f(t) \)[/tex] represents the number of units produced by a company at a time [tex]\( t \)[/tex], where [tex]\( t \)[/tex] is the number of years after the company opened.
2. Identify the starting point: The problem states that the company opened in 2005. This means when [tex]\( t = 0 \)[/tex], it corresponds to the year 2005.
3. Determine what [tex]\( t = 6 \)[/tex] represents: If [tex]\( t = 6 \)[/tex], this represents 6 years after the year 2005. To find out which year this is, you simply add 6 to 2005:
[tex]\[
2005 + 6 = 2011
\][/tex]
4. Interpret [tex]\( f(6) = 44,500 \)[/tex]: Given [tex]\( f(6) = 44,500 \)[/tex], this means that in the year 2011, the company produced 44,500 units.
So, the correct interpretation of the statement [tex]\( f(6) = 44,500 \)[/tex] is:
In 2011, 44,500 units are produced.
1. Understand the function notation: The function [tex]\( f(t) \)[/tex] represents the number of units produced by a company at a time [tex]\( t \)[/tex], where [tex]\( t \)[/tex] is the number of years after the company opened.
2. Identify the starting point: The problem states that the company opened in 2005. This means when [tex]\( t = 0 \)[/tex], it corresponds to the year 2005.
3. Determine what [tex]\( t = 6 \)[/tex] represents: If [tex]\( t = 6 \)[/tex], this represents 6 years after the year 2005. To find out which year this is, you simply add 6 to 2005:
[tex]\[
2005 + 6 = 2011
\][/tex]
4. Interpret [tex]\( f(6) = 44,500 \)[/tex]: Given [tex]\( f(6) = 44,500 \)[/tex], this means that in the year 2011, the company produced 44,500 units.
So, the correct interpretation of the statement [tex]\( f(6) = 44,500 \)[/tex] is:
In 2011, 44,500 units are produced.
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