For decay rates/decay factors in functions:
The decay rate is the actual amount you are substituting into an
equation. For example, a common exponential function such as
"y=a(b)^x" would show exponential decay if it were written as
"y=i(1-r)^t".
"i" represents the initial amount, such as in the previous
example, would be $100. "(1-r)" is the decay factor, whereas the
"r" is your decay rate. The decay factor is derived from 1-r
because a function would only be considered decaying if the
growth/decay factor is less than 1. Another way of looking at this
principal is if we were to say a car we bought lost 8% of its value
every year. Then it would only be retaining 92% of it's initial
value. "t" is your time unit, or the number of times the function
is applied.
Example:
A medical patient is given 400 mg of antibiotics. Say that 10%
of the medicine given to a patient is eliminated by the patient's
body every 2 hours. How much medicine will remain in the patient's
blood stream in 4 hours?
Sample equation: y=i(1-r)^t --> "i" in this case would be
400, or the 400 mg given to the patient on. (1-r) would be 1-10% or
1-0.10 -- the amount of antibiotic that will remain in the patients
body. "t" in this case would be 2, because the eliminated amounts
are only calculated in 2 hour increments, with 4 hours total in the
problem.
Your equation: y=400(1-0.10)^2
y=400(0.90)^2
y=400(0.81)
y=324 mg of antibiotics left in the blood stream
