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You can write an exponential curve in the form:y = A e^(Bx) And also in the form: y = C D^x Where A, B, C, and D are constants, and "^" represents a power. Also, with exponential growth, the function will increase or decrease by the same factor in equal time intervals (for example, double every 1.3 years; triple every 2 months; etc.).
If the common ratio is negative then the points are alternately positive and negative. While their absolute values will lie on an exponential curve, an oscillating sequence will not lie on such a curve,
The linear function changes by an amount which is directly proportional to the size of the interval. The exponential changes by an amount which is proportional to the area underneath the curve. In the latter case, the change is approximately equal to the size of the interval multiplied by the average value of the function over the interval.
In mathematics, a asymptote is a straight line that a curve approaches but never quite reaches. Asymptotes can occur in various mathematical functions, such as rational functions or exponential functions. They are used to describe the behavior of a function as the input approaches infinity or negative infinity.
It is a bit like an s-curve. See it for yourself at the following link.