Answer :
To solve the problem and interpret the meaning of [tex]\( f(6) = 44,500 \)[/tex], we need to consider what each part of this notation represents. Here's a detailed, step-by-step explanation:
1. Understanding the Function Notation:
- The function [tex]\( f(t) \)[/tex] represents the number of units produced by a company [tex]\( t \)[/tex] years after it opened.
2. Identifying the Start Year:
- The company opened in 2005.
3. Analyzing the Given Expression [tex]\( f(6) = 44,500 \)[/tex]:
- The notation [tex]\( f(6) \)[/tex] indicates that we are looking at the number of units produced 6 years after the company opened.
4. Calculating the Year:
- Since the company opened in 2005, and we are interested in production 6 years after opening:
- Add the 6 years to the opening year:
[tex]\[ 2005 + 6 = 2011 \][/tex]
- So, 6 years after the company opened is the year 2011.
5. Interpreting the Statement [tex]\( f(6) = 44,500 \)[/tex]:
- The number [tex]\( 44,500 \)[/tex] represents the units produced in that particular year.
- Therefore, in the year 2011, the company produced 44,500 units.
In conclusion, the correct interpretation of [tex]\( f(6) = 44,500 \)[/tex] is: "In 2011, 44,500 units are produced."
1. Understanding the Function Notation:
- The function [tex]\( f(t) \)[/tex] represents the number of units produced by a company [tex]\( t \)[/tex] years after it opened.
2. Identifying the Start Year:
- The company opened in 2005.
3. Analyzing the Given Expression [tex]\( f(6) = 44,500 \)[/tex]:
- The notation [tex]\( f(6) \)[/tex] indicates that we are looking at the number of units produced 6 years after the company opened.
4. Calculating the Year:
- Since the company opened in 2005, and we are interested in production 6 years after opening:
- Add the 6 years to the opening year:
[tex]\[ 2005 + 6 = 2011 \][/tex]
- So, 6 years after the company opened is the year 2011.
5. Interpreting the Statement [tex]\( f(6) = 44,500 \)[/tex]:
- The number [tex]\( 44,500 \)[/tex] represents the units produced in that particular year.
- Therefore, in the year 2011, the company produced 44,500 units.
In conclusion, the correct interpretation of [tex]\( f(6) = 44,500 \)[/tex] is: "In 2011, 44,500 units are produced."
