Question

How do I find the multiplier for a rate of exponential decay?

Answer 1

This depends on what you already know. I'll do two examples:

First to know :
Decay follows the formula: `N=B*g^t`
Where `N`=new situation after `t` periods. `B`=start value
`g`="growth" factor and must be `<1` to be called decay

Simple :
You know that decay is 5% per period. So after each period the value is only 95% of the period before. You "growth" (decay) factor is then `95//100=0.95`

Bit more complicated:
A radio-active object has a half-life of 4 days, what is the decay-factor (per day)?

`N=B*g^t` fill in what you know:
`0.5=1*g^4->g^4=0.5->g=root 4 0.5~~0.841`

Which means it will lose almost 16% of its activity per day (check!)

Extra :
Instead of using `root t x` you may use `x^(1//t)` on your calculator
You key in x^(1/t) with the right numbers, e.g. 0.5^(1/4)