Question

A patient is given a 100-milligram dosage of a drug that decays exponentially at a rate of 11% per hour. The doctor wants to know when 15 milligrams of the drug remains.
Write an equation that models the situation. Explain each aspect of your equation.

Answer 1

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: