Answer:
This is an example of exponential decay (somewhat similar to half-life).
If it decays at 11% per hour we can calculate its half-life by this formula:
half life = [ time • ln (2) ] ÷ ln (beginning amount ÷ ending amount)
where "ln" means natural log
half life =[ 1 hour * .69315] / ln (100 / 89)
half life =[.69315] / ln (1.1235955056)
half life =[.69315] / 0.11653381624
half life = 5.9481 hours
We need "lambda" "λ" (the decay constant) which equals
λ = ln(2) / half-life = .693147 / 5.9481 = 0.1165325062
Now we need a formula for the time required:
time = ln (Nt ÷ N0) ÷ -λ where No = beginning amount (100 milligrams) Nt = ending amount (15 milligrams)
time = ln (15 ÷ 100) ÷ -0.1165325062
time = ln (.15) / -0.1165325062
time = -1.8971199849 / -0.1165325062
time = 16.2797492885 hours
Source: https://www.1728.org/halflif2.htm
Step-by-step explanation:
