algebra word problem-cell phone bills?

Question

suppose that the charges for a cell phone bill are $0.50 for the first minute and $0.25 for each additional minute. assume that a fraction of a minute is rounded up. how do i find a formula for a function "f" that computes the cost of a call that is "x" minutes long, where 0 < x <= 5? but writing it in a piecewise-constant fuction?

an explanation would be greatly appreciated and thanks for the help.

Answer 1

Cost = 0.50 + 0.25([x]-1)

Where 0.50 is the cost for the first minute, [] is the ceiling of x(smallest integer greater than or equal to x), x is the number of minutes spent talking (-1 to discount the first minute, which is already included) and 0.25 is the cost of each additional minute.

However, the following should also work:

Cost = 0.25([x]+1)

Answer 2

f(x) = 0.5 + (x - 1) * 0.25

Explanation:
0.5 represents the first minute charge. x - 1 represents "the next minute". It is substracted by 1 because we already add 0.5 as the first minute charge. Got it?