The fee to park in the parking lot of a shopping mall cost 40.00 for the first two hours and an extra 10.00 for each hour or fraction of it after that. If you park for more than twelve hours you instead pay a flat of 200.00 represent your parking fee using the function p(t) where t is the number of hours you parked in the mail
To represent the parking fee using the function p(t), where t is the number of hours parked in the mall, we need to account for the different fee structures based on the number of hours parked.
For the first two hours, the fee is a flat rate of $40.00. So, if t ≤ 2, we have:
p(t) = $40.00
After the first two hours, the fee increases by $10.00 for each hour or fraction of it. So, if t > 2, we need to calculate the additional fee based on the remaining time.
If t ≤ 12, the additional fee is given by:
Additional fee = $10.00 × (t - 2)
If t > 12, the flat rate of $200.00 applies:
Additional fee = $200.00
Therefore, the complete function p(t) to represent the parking fee is:
If t ≤ 2:
p(t) = $40.00
If 2 < t ≤ 12:
p(t) = $40.00 + $10.00 × (t - 2)
If t > 12:
p(t) = $200.00
Example:
If you parked for 5 hours, we plug in t = 5 into the function:
p(5) = $40.00 + $10.00 × (5 - 2) = $40.00 + $30.00 = $70.00
Note: The function assumes that the fee calculation is continuous and doesn't account for partial hours.