To address the problem, let's follow a step-by-step process.
Firstly, we want to determine how many steps Eric needs to walk each day to reach his goal. Given:
- The total number of steps Eric wants to walk is 24,000.
- He wants to achieve this in 4 days.
We calculate the number of steps he needs to walk each day by dividing the total steps by the number of days:
[tex]\[
\text{Steps per day} = \frac{24000 \text{ steps}}{4 \text{ days}} = 6000 \text{ steps/day}
\][/tex]
Next, we need to establish the function [tex]\( y \)[/tex] that represents the number of steps Eric still needs to walk, [tex]\( y \)[/tex], with respect to the number of days since he started, [tex]\( x \)[/tex].
- After [tex]\( x \)[/tex] days, Eric has walked [tex]\( x \times 6000 \)[/tex] steps.
- Therefore, the remaining number of steps to reach his goal is the total steps minus the number of steps he has already walked:
[tex]\[
y = 24000 - (6000 \times x)
\][/tex]
Simplify the equation:
[tex]\[
y = 24000 - 6000x
\][/tex]
The function [tex]\( y = 24000 - 6000x \)[/tex] can also be written as:
[tex]\[
y = -6000x + 24000
\][/tex]
Now, let's match this function to the options provided:
A. [tex]\( y = 8000x - 24000 \)[/tex] (Incorrect)
B. [tex]\( y = -8000x + 24000 \)[/tex] (Incorrect)
C. [tex]\( y = 6000x - 24000 \)[/tex] (Incorrect)
D. [tex]\( y = -6000x + 24000 \)[/tex] (Correct)
Therefore, the correct answer is:
[tex]\[
\boxed{D \text{.} \, y = -6000x + 24000}
\][/tex]
