The discussion revolves around finding an algebraic equation that expresses the value of B in relation to A on a Cartesian plane, specifically when A is defined as a horizontal line at y=1. The user seeks a formula for B that starts at the origin (0,0) and approaches A at a constant rate. A participant clarifies that the interpretation of "approaches infinite A" is likely a misunderstanding, suggesting that B can be modeled using the equation y=1+Ce^{\alpha x}, where α is a negative constant, indicating that B asymptotically approaches y=1 as x increases.
PREREQUISITESMathematicians, students studying calculus and differential equations, and anyone interested in algebraic modeling of functions in relation to Cartesian coordinates.
a.k.a. The Cartesian Plane. Probably the most widely known and frequently used coordinate system in Mathematics
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 [itex]\alpha[/itex], any solution to that is of the formseasnake said: