A mathematics superhero? Comic book and mathematics problem needs a solution!!!

Hi everyone!

I have a little problem here that I am trying to work out but I can't solve... Really the problem here is that I'm a terrible Mathematicain! But I'm here to learn!!!!

The problem is simple (or at lease simply explained) and I have included a piece of a larger table (attached xls) that has all the informatio.


I run a comic book shop and I am developing a website for selling the comics. Unfortunately I have to input the prices of the comics manually. My web developer has made things easier for me by creating a program that allows me to input the prices. Now, there is a price guide that I am using but there are some problems. First of all, there are 17 different grades for the comics (ie, NM+, mn, mn- vf+, vf,vf-) and so on. Now, the guide lists the prices in NM-, VF, f, VG and G. When I looked closely at the prices I realised that there was not a constant relationship between the values. For example, when a comic is valued at $3 NM-, the price of the same comic in the condition VF is 66% of the NM- price. But when the comic is priced at $100 NM- the VF price is only 45% of this value.

The table below states the different values of NM-, beneath that is the percentage (expressed in decimal form) of that value. So what I was looking for was a formula to determine the percentages of the lower grades when the NM- value is input. The goal is to be able to integrate this formula into my website so I can accurately price all the comics.

If anyone could show me how to solve this problem or even point me in the right direction I would be truly grateful as it would be a tremendous help!!!

Thanks in advance!!!!

NM-	3	5	8	10	15	25	30	40	50	60	65	75	90	105
VF	0.66	0.64	0.625	0.6	0.6	0.56	0.5333	0.5	0.48	0.46666	0.4615	0.4533	0.45555	0.4476
F	0.46	0.46	0.45	0.45	0.4	0.36	0.3	0.225	0.24	0.0234	0.2307	0.2133	0.2	0.2
VG	0.265	0.25	0.25	0.25	0.245	0.24	0.2	0.15	0.16	0.155	0.15	0.14666	0.133	0.1333333
G	0.13	0.127	0.125	0.125	0.1225	0.12	0.1	0.075	0.08	0.0782	0.0769	0.07333	0.07222	0.0666666

Here is a plot of the values for VF, F, VG, G with respect to the logarithm of the NM- values

Attachment 24525

As you can see, the relationship is not simple, and it's not linear either. The picking of these values is quite weird. Can you elaborate how the VF, F, VG, G values were determined in general?