a taxi fare of davao city costs P40.00 for the first kilometer and extra P10.00 every kilometer. if you travel six hours instead you pay a flat rate of P10.00. Represent your fare using the function f ( t ) where t is the number of hours you pay the fare.
To represent the fare using the function f(t), where t is the number of hours you pay the fare, we can break down the fare into two parts: the fare for traveling less than six hours and the flat rate for traveling six hours or more.
For traveling less than six hours, the fare is calculated based on the distance. The fare for the first kilometer is P40.00, and for every additional kilometer, it is an extra P10.00. Since 1 kilometer is covered in approximately 12 minutes (6 kilometers per hour), we can calculate the number of kilometers traveled based on the number of hours.
Let's derive the formula for the fare based on the number of hours t, where t < 6:
1. Calculate the number of kilometers traveled: km = t * 6
(As mentioned earlier, the taxi covers 6 kilometers per hour)
2. Calculate the fare based on the number of kilometers traveled: fare = P40 + P10 * (km - 1)
Now, for traveling six hours or more, the fare is a flat rate of P10.00. If t ≥ 6, then the fare is simply P10.00.
To represent the fare using the function f(t), we can express it as follows:
f(t) = {
fare = P40 + P10 * (km - 1) if t < 6
fare = P10 if t ≥ 6
}
For example, if you traveled for 4 hours (t = 4), the fare would be calculated as follows:
km = 4 * 6 = 24 kilometers
fare = P40 + P10 * (24 - 1) = P40 + P230 = P270
So, f(4) = P270.