An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Analyze the given table to extract the cost for different time intervals.
Create a piecewise function C(t) that models the cost of renting skates for t hours.
Compare the derived function with the function provided in the question and identify the differences.
Conclude that the function provided in the question is incorrect and provide the correct piecewise function: C ( t ) = ⎩ ⎨ ⎧ 5 10 20 25 if 0 < t ≤ 1 if 1 < t ≤ 2 if 2 < t ≤ 5 if 5 < t ≤ 24 .
Explanation
Understanding the Problem We are given a table that shows the cost of renting roller skates for different time intervals. We need to find a function that models this situation, where c is the cost in dollars and t is the number of hours the skates are rented for in a single day.
Extracting Information from the Table The table gives us the following information:
Up to 60 minutes (1 hour): $5
Up to 2 hours: $10
Up to 5 hours: $20
Daily: $25
Creating the Piecewise Function We can write a piecewise function C ( t ) to model the cost of renting skates for t hours:
C ( t ) = ⎩ ⎨ ⎧ 5 10 20 25 if 0 < t ≤ 1 if 1 < t ≤ 2 if 2 < t ≤ 5 if 5 < t ≤ 24
Note that the daily rate applies for any time greater than 5 hours, up to 24 hours (a full day).
Comparing with the Given Function Now, let's compare the function we derived with the function provided in the question:
C(t)=\left{\begin{array}{r} 5 \text { if } 0
