"A fix it business charges 40 dollars per hour or any fraction thereof. Write a step function for the costs up to 3 hours." I'm not sure how to go about this...I know that it's a step function, but I'm not sure how I would go about writing it. Help ASAP please! Thank you so much!
To write a step function for the costs up to 3 hours, we need to consider how the cost changes based on the number of hours. In this scenario, the fix it business charges $40 per hour or any fraction thereof.
Let's break it down step by step:
1. Identify the intervals: Each hour or any fraction thereof corresponds to an interval. Since the cost changes after each hour or fraction thereof, we need to consider separate intervals up to 3 hours.
2. Determine the cost within each interval: For each interval, we need to calculate the cost based on the number of hours. If the interval is less than an hour, we will consider it as a fraction thereof and calculate the cost accordingly.
3. Write the step function: Once we have determined the cost within each interval, we can write the step function.
Let's go through each step in detail:
1. Identify the intervals:
Since we need to calculate the cost up to 3 hours, we will have four intervals:
- Interval 1: 0 to 1 hour
- Interval 2: 1 to 2 hours
- Interval 3: 2 to 3 hours
2. Determine the cost within each interval:
- Interval 1 (0 to 1 hour): The cost for this interval will be $40 because it is based on a full hour.
- Interval 2 (1 to 2 hours): The cost for this interval will also be $40 as it is based on a full hour.
- Interval 3 (2 to 3 hours): The cost for this interval will be $80, as it includes two full hours.
3. Write the step function:
Now, let's write the step function based on the intervals and their respective costs:
- For 0 ≤ x < 1: f(x) = $40
- For 1 ≤ x < 2: f(x) = $40
- For 2 ≤ x ≤ 3: f(x) = $80
In this step function, x represents the number of hours, and f(x) represents the cost for that number of hours.
So, the step function for the costs up to 3 hours is:
f(x) = $40 for 0 ≤ x < 1
f(x) = $40 for 1 ≤ x < 2
f(x) = $80 for 2 ≤ x ≤ 3
I hope this helps! Let me know if you have any further questions.