At a certain marathon race, the winner comes in at a time of 130 minutes. Second place comes in at a time of 135 minutes, and third place comes in at 140 minutes. Starting with third place, contestants come in at regular intervals all the way up to the last successful finisher, who gets 10th place with a time of 168 minutes.

Create a piecewise function

If x is the place to finish, and t is the time,

t(x) = 125+5x for x=1,2,3
t(x) = 140+(168-140)/(10-3) x for x>3
= 140+4x

Thank you:)

To create a piecewise function for the given scenario, we need to represent the placement (x) and corresponding time (y) for each contestant. Let's analyze the information given and break it down step by step:

1. The winner comes in at a time of 130 minutes. This means the first-place finisher finishes at time 130.
So, for the first-place finisher: y = 130

2. The second-place finisher comes in at a time of 135 minutes. Since the time for each successive finisher increases by a regular interval, we can deduce that the second-place finisher's time is 135 and the interval is 5 minutes.
So, for the second-place finisher: y = 135

3. The third-place finisher comes in at a time of 140 minutes. Again, using the interval of 5 minutes, we can determine the third-place finisher's time and so on.
So, for the third-place finisher: y = 140

4. Continuing this pattern, we can determine the time for each successive finisher:
For the fourth-place finisher: y = 140 + 5
For the fifth-place finisher: y = 140 + 2 * 5
For the sixth-place finisher: y = 140 + 3 * 5
For the seventh-place finisher: y = 140 + 4 * 5

5. The last successful finisher gets 10th place with a time of 168 minutes. Therefore, we can determine the time for each successive finisher:
For the eighth-place finisher: y = 140 + 5 * (8 - 3)
For the ninth-place finisher: y = 140 + 5 * (9 - 3)
For the tenth-place finisher: y = 140 + 5 * (10 - 3)

Putting it all together, we have a piecewise function:

f(x) = {
130, x = 1
135, x = 2
140, x = 3
140 + (x - 3) * 5, 4 ≤ x ≤ 7
140 + 5 * (x - 3), 8 ≤ x ≤ 10
}

This function represents the placement (x) and corresponding time (y) for each contestant in the marathon race.