Modifying the curve of Exp. Growth

[Sabrecho]

I have a little problem. I need a formula that can be coded into a spreadsheet to produce the cost of a given Stat score. As the score increases, the cost to take it to the next level should get progressively more expensive. On the other hand, very early stages of score increases should still be manageable.

In other words, it should remain a relatively low cost to buy a score of up to 6 but then become gradually more expensive.

As a point of reference, I'm including a graph that shows the closest kind of formula I can think of (blue) and the desired result (red). What produces the blue line for me is (x^Factor)+Floor, where Factor = 1.45 and Floor = 5. (The red line was produced using manually entered test data.)

Thanks in advance for your help.

 

[tkhunny]

Is this part of your business plan? Looks a lot like cheating.

Why not try an Exponential, rather than the Power function you have defined?

 

[Sabrecho]

Is this part of your business plan? Looks a lot like cheating.

Why not try an Exponential, rather than the Power function you have defined?

I beg pardon, TK, but who said "Business Plan"?? This is for
the Character Stats on a Role Playing Game.

Also, I'm looking for this exponential growth cost formula to
Prevent Cheating by making it more costly to get into super-
human stat values, compared to advancing from teenager to
adult level stats.

Now, I hope you'll bear with me since it's been more than 20 years
since high-school, but isn't "Exponential" and "Power" the same thing?

 

[mmm4444bot]

… isn't "Exponential" and "Power" the same thing?

Not when you're talking about function types.

In a power function, the input variable is the base.

In an exponential function, the input variable is the exponent.

Simple examples:

y = x^2 (power function)

y = 2^x (exponential function)

For your task, you can use exponential regression, to obtain an exponential function of this form:

y = a*b^x

Regression will give you the values of a and b, generating an exponential curve that fits your data points as close as possible (i.e., minimized error)

You can input your data points at a regression calculator here:

http://keisan.casio.com/exec/system/14059930973581

For example, I estimated five (x,y) points from your red curve, and got the following result.

(0, 5)
(6, 10)
(9, 20)
(11, 30)
(12, 40)

The regression calculator gave a = 4.432 and b = 1.189 (both rounded)

Therefore, the exponential function is y = 4.432*1.189^x.

With actual data (using more than five points), you will get a better result. :cool:

 

[tkhunny]

It was just a question.
No pardon required.

 

[stapel]

I have a little problem. I need a formula that can be coded into a spreadsheet to produce the cost of a given Stat score. As the score increases, the cost to take it to the next level should get progressively more expensive. On the other hand, very early stages of score increases should still be manageable.

For this exercise, how are "progressively more expensive" and "should still be manageable" specifically defined? What specific data points have you been given? What, specifically, did the instructions tell you to do with this information?

In other words, it should remain a relatively low cost to buy a score of up to 6 but then become gradually more expensive.

How do the instructions define "relatively low", "gradually", and "more expensive"? The model (that is, the equation) you develop will depend heavily upon these definitions.

When you reply, please include a clear listing of your thoughts and efforts so far. Also, please explain (your understanding of) how this exercise requires calculus to solve, rather than statistics. Thank you!