Looking for an equation expressed algebriacally that answers the following

[seasnake]

Given an XY graph where the horizontal line is X and the vertical line is Y and their intersection is zero, if A = 0,1 (a horizontal line one increment above the X axis), I want to know the formula that correctly expresses the value of B if B started at 0,0 and always approaches infinite A at a uniformly constant rate.

 

[Mentallic]

Given an XY graph where the horizontal line is X and the vertical line is Y and their intersection is zero

a.k.a. The Cartesian Plane. Probably the most widely known and frequently used coordinate system in Mathematics

Everything is very clear cut, until...

approaches infinite A

eh? Please elaborate.

 

[HallsofIvy]

Given an XY graph where the horizontal line is X and the vertical line is Y and their intersection is zero, if A = 0,1 (a horizontal line one increment above the X axis), I want to know the formula that correctly expresses the value of B if B started at 0,0 and always approaches infinite A at a uniformly constant rate.

You just said "A= 0, 1", a notation I would have interpreted as the point (0, 1) but then you say "(a horizontal line one increment above the X axis)" which is the line y= 1. In either case, what do you mean by "approaches infinite A"? A is NOT "infinite". Do you mean "is asymptotic to y= 1 as x goes to infinity"? And what do you mean by "approaches at a uniformly constant rate"? That d(y-1)/dx= constant? That's impossible. Any solution to that is linear and cannot be asymptotic to y= 1. d(y-1)/dx= constant*(y-1) is possible. Calling the constant rate \alpha, any solution to that is of the form
y=1+ Ce^{\alpha x}
which approaches y= 1 at constant rate \alpha< 0.