It depends on what r stands for.
If r is the radius of a circle or sphere, then yes, it must be non-negative.
If r is one of the polar coordinates it can be zero, but not negative.
If r is the correlation coefficient, it can be zero or negative.
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Absolute value is always the opposite of the number.
A typical formula for exponential decay is y(t) = c*exp(-r*t) , where r > 0. The domain is all reals, and the range is all positive reals, since a positive-base exponential always returns a positive value.
The absolute value will always be positive because if you think about it, the absolute value.
the absolute value of any number is always the positive value of that number absolute value of 0.4 = 0.4
The absolute value of a number is its distance from zero on the number line, so it is always non-negative. When you multiply two nonzero absolute values, you are essentially multiplying two non-negative numbers together. In multiplication, a positive number multiplied by a positive number always results in a positive number, hence the product of two nonzero absolute values is always positive.