A parking fee at SM Lucena costs ₱25.00 for the first two hours and an extra ₱5.00 for each hour of extension. If you park for more than twelve hours, you instead pay a flat rate of ₱100.00. Represent your parking fee using the function p(t) where t is the number of hours you parked in the mall.
To represent the parking fee using the function p(t), where t is the number of hours you parked in the mall, we need to consider the different cases mentioned:
1. For the first two hours: The cost is ₱25.00. This is a flat rate and does not depend on the number of hours you park. So, for 0 ≤ t ≤ 2, the parking fee is ₱25.00.
2. For each additional hour beyond the first two: The cost increases by ₱5.00 for each hour. So, for 2 < t ≤ 12, the parking fee would be ₱25.00 + (₱5.00 * (t - 2)).
3. If you park for more than twelve hours: The parking fee is a flat rate of ₱100.00. So, for t > 12, the parking fee would be ₱100.00.
Putting all these cases together, we can define the function p(t) as follows:
p(t) = ₱25.00, for 0 ≤ t ≤ 2
p(t) = ₱25.00 + (₱5.00 * (t - 2)), for 2 < t ≤ 12
p(t) = ₱100.00, for t > 12
This function represents the parking fee based on the number of hours parked in SM Lucena.