Help on a math/writing problem? please?

Question

alright so i just started algebra 2 this year, and i totally don't understand our first assignment.

How do step functions apply to postage rates?

Include the following in your answer:

*an explanation of why a step function is the best model for this situation, while your gas mileage as a function of time as you drive to the post office cannot be modeled with a step function, and

*a graph of a function that represents the cost of a first-class letter.

if you could just give me the general idea, i could probably figure it out. I'm good at writing, i just don't get how this is a step function...

thanks!!

Answer 1

Step functions are discontinuous at certain points.  In other words, they suddenly "jump up" at some point.  They also are flat in between.  So, essentially, a step function stays the same for some period of time, then jumps up to a new level and stays there for some time.

Postage rates do that.  They stay at (say) 33 cents for a letter for, oh, four or five days anyway, then suddenly it costs 37 cents for a letter.  In this scenario, there was never a time when letters were 33.7 cents.  It just skipped that and went straight to 37.  That's a step.

Time as you drive to the post office, however, is not a step.  If you leave home at 1:00 and get to the post office at 1:15, the clock didn't suddenly jump from one to the other.  Somewhere in between, the clock would have read 1:07.  In fact, it would have read 1:07:33.65748, or any other number between 1:00 and 1:15 that you can imagine.

So:  with step functions, the are values that are simply not in the range, even if values on either side are.  As with the example above, 35 cents is not in the range, even though 33 and 37 are.  With other functions, if two values are in the range, every value between them must be as well.  As with the example above, 1:00 and 1:15 are in the range, so every possible time between them is, too.