Question

The topology taxi company charges 2.60 for the first quarter of a mile and 0.36 for each additional fifth of a mile. Find a linear function which models the taxi fare F as a function of the number of miles driven m

Answer 1

The piecewise function for the taxi fare is:

`F(t) = 2.60\cdot \left(\frac {m}{0.25}\right) ,\, 0\,mi\le m \le 0.25\,mi`

`F(t) = 2.60 + 0.36\cdot \left((m)/(0.2) \right)`,
`m > 0.25\,mi`

Explanation:

We must use the following piecewise function:

(i) The Topology Taxi Company charges 2.60 for the first quarter of a mile:

`F(t) = 2.60\cdot \left(\frac {m}{0.25}\right) ,\, 0\,mi\le m \le 0.25\,mi` (1)

Where:

`F(t)` - Taxi fare, in monetary units.

`m` - Number of miles driven, in miles.

(ii) And 0.36 for each additional fifth of a mile:

`F(t) = 2.60 + 0.36\cdot \left((m)/(0.2) \right)`,
`m > 0.25\,mi` (2)