Originally Posted by
rtaxx
so, then, if it IS a geometric progression, as I suggested, then it ISNT an inverse proportion or it isn't JUST an inverse proportion but an "inverse exponential proportion"?
I mean, if a=bc is equivalent to c=(1/b)a it follows that if a is proportional to c with (nonzero) proportionality constant b, then c is also proportional to a with proportionality constant 1/b. If a is proportional to c, then the graph of a as a function of c will be a straight line passing through the origin with the slope of the line equal to the constant of proportionality: it corresponds to linear growth.
Therefor, if a=b/c is equivalent to a=(1/b)/c it follows that the variable a is inversely proportional to the variable c if there exists a non-zero constant b. The constant can be found by multiplying the original c variable and the original a variable. But the graph of two variables varying inversely on the Cartesian coordinate plane is a hyperbola. The product of the A and C values of each point on the curve will equal the constant of proportionality (B). Since b can NEVER equal zero, the graph will NEVER cross either axis.
However a variable is "exponentially proportional", if a=bcⁿ, that is, if a variable a is exponentially proportional to a variable c, a is directly proportional to the exponential function of c, if there exist non-zero constants b and a. So a increases on the graph as a curve, approaching but never quite touching "infinity" where c makes a straight and precise line inextricably towards zero never quite touching it because of the asymtotic nature of a.
So I am pretty sure we DONT have in inverse proportion, we have an "inverse exponential proportion".... now... what is it they say about inverse exponents?