Discrete or Continuous Problem

Date: 13 Feb 1995 00:56:03 -0500
From: Anonymous
Subject: A math question

Here's the question. 

Mae spends $65 a week on food. After 3 weeks she has 
$415 left in her food budget. What my math class wants 
to know is:  Is this continuous or discrete?

Date: 13 Feb 1995 19:24:48 -0500
From: Dr. Ken
Subject: Re: A math question

Hello there!

I would call this a discrete problem, because the function 
that tells you how much money Mae has is not a 
continuous one.  It goes down by big chunks of $65.  

But you can model the situation by a continuous function.  
If you want to know how much money she started with, 
let $A be the money she starts with and let f[x] be the 
function A - 65x.  Then you know f[3] = A - 65*3 = 415,
so A = 610.  Of course, if you want to find out how much 
money she has after Pi weeks, the formula won't work.  
But it's good enough when you plug in integers, and it 
gets the job done.

-Ken "Dr." Math