College

Select the correct answer.

Let [tex]$f(t)$[/tex] be the number of units produced by a company [tex]$t$[/tex] years after opening in 2005. What is the correct interpretation of [tex]$f(6)=44,500$[/tex]?

A. In 2011, 44,500 units are produced.
B. In 2006, 44,500 units are produced.
C. In 2009, 44,500 units are produced.
D. Six years from now, 44,500 units will be produced.

Answer :

Certainly! Let's interpret the given information step-by-step:

1. Understand the Context: We have a function [tex]\( f(t) \)[/tex] that represents the number of units produced by a company [tex]\( t \)[/tex] years after the company opened in 2005.

2. Interpret [tex]\( f(6) = 44,500 \)[/tex]: This specific information tells us that 6 years after the company opened, the number of units produced was 44,500.

3. Determine the Year Corresponding to [tex]\( t = 6 \)[/tex]: Since the company opened in 2005, we need to calculate the year that is 6 years later.

- Start with the year 2005.
- Add 6 years: [tex]\( 2005 + 6 = 2011 \)[/tex].

4. Summarize the Interpretation: In the year 2011, the company produced 44,500 units.

Therefore, the correct interpretation of [tex]\( f(6) = 44,500 \)[/tex] is:

In 2011, 44,500 units are produced.