Decay rate vs decay factor

Answer 1

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

Answer 2

The decay rate refers to the percentage decrease in a quantity over a given time period. The decay factor, on the other hand, represents the multiple by which a quantity decreases over time, often expressed as a fraction or decimal less than 1. The decay rate is calculated as the difference between 1 and the decay factor, providing complementary perspectives on the same concept of decreasing values.