Alright, let's break down the problem and find the correct function that represents the number of steps Eric still needs to walk to reach his goal.
1. Total Steps and Days:
- Eric has set himself a goal of walking a total of 24,000 steps.
- He plans to achieve this goal in 4 days.
2. Steps Per Day:
- Since Eric wants to distribute his steps evenly over 4 days, we need to calculate how many steps he should walk each day.
- Number of steps Eric should walk per day [tex]\( \text{steps\_per\_day} \)[/tex] is calculated as:
[tex]\[
\text{steps\_per\_day} = \frac{\text{total\_steps\_goal}}{\text{total\_days}} = \frac{24,000}{4} = 6,000 \text{ steps/day}
\][/tex]
3. Function for Steps Remaining:
- Let [tex]\( x \)[/tex] represent the number of days since Eric started his challenge.
- We need a function [tex]\( y \)[/tex] that represents the number of steps Eric still needs to walk to reach his goal after [tex]\( x \)[/tex] days.
- On Day 0 (when he hasn't walked any steps yet), he still needs to walk 24,000 steps.
- Each day, he walks 6,000 steps, so the remaining steps decrease by 6,000 steps per day.
- Thus, the function [tex]\( y \)[/tex] is given by:
[tex]\[
y = \text{total\_steps\_goal} - \text{steps\_per\_day} \times x
\][/tex]
- Substituting the values we calculated:
[tex]\[
y = 24,000 - 6,000 \times x
\][/tex]
Therefore, the correct function that represents the number of steps Eric still needs to walk to reach his goal with respect to the number of days since he started his challenge is:
[tex]\[
D. \ y = -6,000 x + 24,000
\][/tex]
