A parking garage is changing its parking fees for a week long festival. The function below represents the cost to park in the garage as a function of time (days into the festival).
Piece wise
c(t) =
10; 0 <= t <= 2
10; 2 < t <= 5
7; 5 < t <= 7
a) What would be the best days to park in the garage?
b) calculate c(4) - c(2)
To find the best days to park in the garage, we need to determine the days when the parking fees are the lowest.
Looking at the piecewise function provided:
- For 0 <= t <= 2, the cost to park is $10 per day.
- For 2 < t <= 5, the cost to park is also $10 per day.
- For 5 < t <= 7, the cost decreases to $7 per day.
Based on the information above, the best days to park in the garage are during the period when the cost is $7 per day, which is from 5 to 7 days into the festival.
To calculate c(4) - c(2), we need to substitute the values of t into the function and subtract the results:
c(4) = 10, because 2 < 4 <= 5 (falls into the second range).
c(2) = 10, because 0 <= 2 <= 2 (falls into the first range).
Therefore, c(4) - c(2) = 10 - 10 = 0.