Many dynamic processes can be approximated as an exponential decay. This applies to radioactive decay, some chemical reactions, ageing of LEDs etc. See https://en.wikipedia.org/wiki/Exponential_decay for more background.
Assume that the process starts with a normalised value of x(0) = 1, and it follows the following decay law:
x'(t) = - x(t) / tau
where x'(t) is the first derivative of x(t), and time constant tau is 2.
Write a function that returns the value x for a given input t. It should be able to deal with a vector input.
"d/dt x(t)" —> "d{x(t)}/dt". Or write perhaps just "x′(t)".
By the way, as written your tau represents a "decay constant", rather than a "time constant" — it will have dimensions of reciprocal time (assuming that t represents time).
Your Problem Statement and Test Suite appear to be inconsistent. Please check Solution 1404081.
Thanks for the comments - you are indeed correct, and I have rewritten the equation accordingly. I hope it is correct and consistent now.
Thanks for attending to that, Thomas. It looks consistent now.
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