Representing the Number of Steps Left

Oct 13, 2025 by recoveryshake.com 127 views

Eric has set a goal to walk 24,000 steps in 4 days. To achieve this, he plans to walk the same number of steps each day. In this scenario, we need to determine the function that represents the number of steps Eric still needs to walk to reach his goal with respect to the number of days that have passed.

Calculating Daily Steps

To find out how many steps Eric needs to walk each day, we can divide the total number of steps (24,000) by the number of days (4).

24,000 steps / 4 days = 6,000 steps per day

Representing the Number of Steps Left

Let's assume that Eric has already walked for x days. To find the number of steps he still needs to walk, we can subtract the total number of steps he has already walked from the total goal.

Total steps = 24,000 Steps walked in x days = 6,000x

The number of steps Eric still needs to walk is:

24,000 - 6,000x

Function Representation

The function that represents the number of steps Eric still needs to walk to reach his goal with respect to the number of days that have passed is:

f(x) = 24,000 - 6,000x

Graphical Representation

To visualize the function, we can create a graph with the number of days (x-axis) and the number of steps left (y-axis).

Interpreting the Graph

The graph shows that the number of steps Eric still needs to walk decreases as the number of days increases. This makes sense, as Eric is walking the same number of steps each day.

Conclusion

In conclusion, the function that represents the number of steps Eric still needs to walk to reach his goal with respect to the number of days that have passed is f(x) = 24,000 - 6,000x. This function can be used to calculate the number of steps Eric still needs to walk at any given point in time.

Mathematical Representation

Mathematically, the function can be represented as:

f(x) = 24,000 - 6,000x

where x is the number of days that have passed.

Domain and Range

The domain of the function is all real numbers greater than or equal to 0, as Eric cannot walk a negative number of steps. The range of the function is all real numbers greater than or equal to 0, as Eric will always have a positive number of steps left to walk.

Solving for x

To find the number of days it will take Eric to reach his goal, we can set the function equal to 0 and solve for x.

24,000 - 6,000x = 0

Solving for x, we get:

x = 4

This means that Eric will reach his goal in 4 days.

Real-World Applications

This problem has real-world applications in various fields, such as:

Fitness tracking: This problem can be used to calculate the number of steps a person needs to walk to reach their daily goal.
Travel planning: This problem can be used to calculate the number of steps a person needs to walk to reach their destination.
Health and wellness: This problem can be used to calculate the number of steps a person needs to walk to reach their daily step goal.

Conclusion

Q: What is Eric's goal in the walking challenge?

A: Eric's goal is to walk 24,000 steps in 4 days.

Q: How many steps does Eric need to walk each day to reach his goal?

A: To find out how many steps Eric needs to walk each day, we can divide the total number of steps (24,000) by the number of days (4). This gives us 6,000 steps per day.

Q: What is the function that represents the number of steps Eric still needs to walk to reach his goal with respect to the number of days that have passed?

A: The function that represents the number of steps Eric still needs to walk to reach his goal with respect to the number of days that have passed is f(x) = 24,000 - 6,000x.

Q: How can we use the function f(x) = 24,000 - 6,000x?

A: We can use the function to calculate the number of steps Eric still needs to walk at any given point in time. For example, if Eric has already walked for 2 days, we can plug in x = 2 into the function to find the number of steps he still needs to walk.

Q: What is the domain of the function f(x) = 24,000 - 6,000x?

A: The domain of the function is all real numbers greater than or equal to 0, as Eric cannot walk a negative number of steps.

Q: What is the range of the function f(x) = 24,000 - 6,000x?

A: The range of the function is all real numbers greater than or equal to 0, as Eric will always have a positive number of steps left to walk.

Q: How can we solve for x in the function f(x) = 24,000 - 6,000x?

A: To solve for x, we can set the function equal to 0 and solve for x. This gives us x = 4, which means that Eric will reach his goal in 4 days.

Q: What are some real-world applications of the function f(x) = 24,000 - 6,000x?

A: Some real-world applications of the function include:

Fitness tracking: This function can be used to calculate the number of steps a person needs to walk to reach their daily goal.
Travel planning: This function can be used to calculate the number of steps a person needs to walk to reach their destination.
Health and wellness: This function can be used to calculate the number of steps a person needs to walk to reach their daily step goal.

Q: What is the significance of the function f(x) = 24,000 - 6,000x in the context of Eric's walking challenge?

A: The function f(x) = 24,000 - 6,000x represents the number of steps Eric still needs to walk to reach his goal with respect to the number of days that have passed. This function can be used to calculate the number of steps Eric still needs to walk at any given point in time.

Q: How can we use the function f(x) = 24,000 - 6,000x to make predictions about Eric's walking challenge?

A: We can use the function to make predictions about Eric's walking challenge by plugging in different values of x into the function. For example, if Eric has already walked for 3 days, we can plug in x = 3 into the function to find the number of steps he still needs to walk.

Q: What are some potential limitations of the function f(x) = 24,000 - 6,000x?

A: Some potential limitations of the function include:

Assuming a constant rate of walking: The function assumes that Eric walks at a constant rate of 6,000 steps per day. However, this may not be the case in reality.
Not accounting for rest days: The function does not account for rest days, which may be necessary for Eric to recover from his walking challenge.
Not considering external factors: The function does not consider external factors that may affect Eric's walking challenge, such as weather or terrain.