Exponential graphing/formula: increasing base, doubling cost

[actondenton]

So I used to be pretty good at math, now that I've been out of school for a few years I've forgot everything (basically). I've worked the last few hours trying to write a formula for this relation:

Base = 10

For each time the increase is greater than 1/2 the base, the cost to increase doubles. So for the first 5 the cost is 1, for the next 5 the cost is 2, the next 5 the cost is 4, then next 5 the cost is 8 etc etc etc.

At first I tried making this an exponential graph, and when my base was 1 I'd come up with Y=2^X. However when I used different coordinates or bases it didn't work. Honestly though I'm not even sure that Y=AB^X is the formula I should be using...so basically I am stuck. Any hints?

 

[brandy]

Do you have an actual table of values to use to get your exponential equation?

 

[Denis]

You're not being very clear.

5   10   15   20   25 ....
1    2    4    8   16 ....

Looks like that's what you're getting at.
Is your question: given the base, what is the cost?
If so (let b = base):
cost = 2^(b/5 - 1)

Example: b = 20
cost = 2^(20/5 - 1) = 2^(4 - 1) = 2^3 = 8

 

[actondenton]

Sorry for not being clear, but I was trying to get the type of formula to use for this relation.

base	10			

Iteration	Set count	Cost each	Cost per set	Total spent
1	               5	          1	           5	             5
2	               5	          2	           10	            15
3	               5	          4	           20	            35
4	               5	          8	           40	            75
5	               5	          16	          80	            155
6	               5	          32	          160	           315
7	               5	          64	          320	           635
8	               5	          128	         640	          1275
9	               5	          256	         1280            2555

So my goal is to know what the total volume I can get for a specific cost (my base will be variable, 10 is just an example). In other words if its a base 10 and I spend 75 I know I've acquired 20 plus the original 10. (Edited my numbers)