Question

A taxi charges $20 flat fee for the first 5 miles (even if it takes the rider one mile, it costs $20) and after that the additional miles cost $1.20 per mile. A trip that covers 7 miles will cost $22.40. Write a piece-wise function for the cost of the cab ride. Assume the miles will be whole numbers.

Answer 1

Ok so, we have the fact that 1.20 per mile
Lets represent m as each additional mile
so we have 1.20m which is That much per additional mile
So For the first 5 functions we have
f(1) = 20
f(2) = 20
f(3) = 20
f(4) = 20
f(5) = 20
Only for the first 5 miles though, since it is a flat fee.
So for the additional miles we go back to what I said in the first Paragraph.
1.20m
That is for additional miles, so that will be added to 20
So if you travel more than 5 miles the function looks like this:
f(x) = 20 + 1.20m
So the first 5 miles it is:
f(x) = 20

For 7 mles the function would look like:
f(7) = 20 + 1.20(2)
It is a 2 because it is the additional mile, which is 2
Do you get it? c:

Answer 2

Let d be the distance.
If d<=5 then $5 else ( $5 + $1.20 * Ceiling[ d - 5 ] )
where Ceiling is a function that gives the smallest integer greater than or equal to (d - 5).

Answer 3

In other words, it is assumed that a 6.7 mile trip will cost 5 + 2 * 1.20 dollars.