What is an example of a value of b for which $y=b^x$ represents an exponential decay?

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Answer 1 · 2016-11-09T14:22:33

Any $b in (0, 1)$

With $b > 0, b^x > 0$ and

$y=b^x$ represents decay for b < 1.

Proof:

y'=b^x/ln b < 0, as ln b < 0.

So, y is a decreasing function.

Example:

$(x, (0.1)^x) ... : (-2, 100) (-1, 10) (0, 1) (1, 0.1) (2, 0.01) ...$

What is an example of a value of b for which y=b^xy=b^x represents an exponential decay?