Explain what exponential decay is
2 answers:
A quantity X follows an exponential decay (decrease) if it decreases at a rate proportional to its current value. This can be written as
with t being the time (can be continuous or discrete steps), and "a" being a rate of decay (the larger "a" the faster the decay). X0 is an initial (at time 0) value of the quatity X. Exponential decay is seen frequently in nature (radioactivity, chemical reactions) and economics.
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Looks like your function is
Rewrite it as
Recall that for , we have
If we replace with
, we get
By the ratio test, the series converges if
Solving for gives the interval of convergence,
We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.