# Thread: From A to B, exponentially

1. ## From A to B, exponentially

moderators if this isn't the appropriate sub forum please redirect the post, thanks)
Hello friends

Say I have two values A and B; I also have a given number of days (or "steps"), nominated Z. to reach from A to B by any mathematical operation. if I wanted to do it linearly the equation would be
(A-B)/Z would give me the subtraction element I must subtract from A every day to reach B in Z days.
let
A = 1.6
B = 1
Z = 25 (these are my actual numbers I need to calculate btw)
so (1.6-1)/25 = 0.024 is my answer.

BUT what if I need to get to value B exponentially, so that the rate of change is increasing with every day passing? how do I solve that?

thanks!

2. ## Re: From A to B, exponentially

You can use:

$\displaystyle R = (\frac B A)^{1/Z}$

Then for each step you multiply the previous step by R. For example; if A = 3 and B = 7, and you want to get from A to B in four steps (Z=4) this equation yields:

$\displaystyle R = (\frac 7 3 })^{1/4} = 1.236$

and the steps are;

3,
3 x 1.236 = 3.708,
3.708 x 1.236 = 4.582,
4.582 x 1.236 = 5.664,
5.664 x 1.236 = 7