Numbers that are raised to an exponent either increase or decrease at an extremely fast rate.
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I think you mean 'exponential'. , which means to increase at an increasing rate.
Where the exponential pdf is f(x) = L*exp(-Lx), the standard deviation is 1/L and is the same as the mean of the distribution. See related link.
In a scatter plot that is an exponential model, data can appear to be growing in incremental rates. In this type of model the data will only cross the Y-axis at one point.
A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.
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