How to calculate values ​​based on half-life information?

Question

Mathematics

There is a value that must be reduced in time, so that its value changes by half in the specified number of seconds.

Those. in the settings, the user sets half-life, say 156 seconds - for so much, the T value should fall by half, as with half-life or half-life. Those. after 156 seconds T == T/2, and after 312 seconds T == T/4
Damn, how to calculate this? Those. how to calculate target T after 1 second, after 2 and so on...

Answer 1

K = 0.5 ^1/156 = 0.9955666
T ₁ = T ₀ *K ¹ = 0.9955666 T
T ₂ = T ₀ *K ² = 0.9911529 T
T ₁₀₀₀ = T ₀ *K ¹⁰⁰⁰ = 0.01175765 T
...