Let's break down and solve this step by step.
1. Identify the first drop-down menu:
- The function \( y = 0.75x \) indicates the percentage of work done over \( x \) weeks.
- The value \( 0.75 \) represents the rate of work completion per week. In other words, Ed completes 75% of the work each week.
Therefore, the value 0.75 represents the rate of work completion per week.
2. Determine the function for the percentage of work remaining:
- The work remains can be found by subtracting the percentage of work done from the total work (100% or 1.0 in fractional terms).
- The original function for work done is \( y = 0.75x \).
- The corresponding function for work remaining is \( y = 1 - 0.75x \).
So, the function representing the percentage of work that remains in terms of the number of weeks since the project started is \( y = 1.0 - 0.75x \).
3. Fill in the third drop-down menu:
- From the function representing the work remaining, \( y = 1.0 - 0.75x \), we see the coefficient of \( x \) is \( 0.75 \).
Given these explanations:
- The value 0.75 represents the rate of work completion.
- The function representing the percentage of work that remains is \( y = 1.0 - 0.75x \).
Let's fill in the drop-down menus accordingly:
1. The value 0.75 represents: the rate of work completion per week.
2. The function representing the percentage of work that remains is: \( y = 1.0 - 0.75x \).
So, the complete selections would be:
Ed is managing a construction project. The function \( y=0.75 x \) represents the percentage of work done in terms of the number of weeks since the project started.
The value 0.75 represents [tex]\( \boxed{\text{the rate of work completion per week}} \)[/tex]. The function representing the percentage of work that remains in terms of the number of weeks since the project started is [tex]\( y= \boxed{1.0} \boxed{- 0.75x} \)[/tex].
