Answer :
- $f(t)$ represents the number of units produced $t$ years after 2005.
- $f(6) = 44,500$ means we need to find the year that is 6 years after 2005.
- Calculate the year: $2005 + 6 = 2011$.
- Therefore, in 2011, 44,500 units were produced. The answer is: In 2011, 44, 500 units are produced. $\boxed{In 2011, 44, 500 units are produced.}
### Explanation
1. Understanding the Problem
We are given that $f(t)$ represents the number of units produced $t$ years after the company opened in 2005. We are also given that $f(6) = 44,500$. This means that 6 years after 2005, the company produced 44,500 units.
2. Calculating the Year
To find the year when $t=6$, we add 6 to the year the company opened, which is 2005. So, the year is $2005 + 6 = 2011$.
3. Interpreting the Result
Therefore, $f(6) = 44,500$ means that in 2011, the company produced 44,500 units.
4. Final Answer
The correct interpretation of $f(6) = 44,500$ is that in 2011, 44,500 units were produced.
### Examples
Understanding functions like $f(t)$ is crucial in business. For instance, a store owner might use $f(t)$ to predict sales $t$ months after a marketing campaign. If $f(3) = 500$, it means three months after the campaign, they expect to sell 500 items. This helps in planning inventory and staffing.
- $f(6) = 44,500$ means we need to find the year that is 6 years after 2005.
- Calculate the year: $2005 + 6 = 2011$.
- Therefore, in 2011, 44,500 units were produced. The answer is: In 2011, 44, 500 units are produced. $\boxed{In 2011, 44, 500 units are produced.}
### Explanation
1. Understanding the Problem
We are given that $f(t)$ represents the number of units produced $t$ years after the company opened in 2005. We are also given that $f(6) = 44,500$. This means that 6 years after 2005, the company produced 44,500 units.
2. Calculating the Year
To find the year when $t=6$, we add 6 to the year the company opened, which is 2005. So, the year is $2005 + 6 = 2011$.
3. Interpreting the Result
Therefore, $f(6) = 44,500$ means that in 2011, the company produced 44,500 units.
4. Final Answer
The correct interpretation of $f(6) = 44,500$ is that in 2011, 44,500 units were produced.
### Examples
Understanding functions like $f(t)$ is crucial in business. For instance, a store owner might use $f(t)$ to predict sales $t$ months after a marketing campaign. If $f(3) = 500$, it means three months after the campaign, they expect to sell 500 items. This helps in planning inventory and staffing.
