Continuous Exponential Decay: Final Value
How to find the final value of continuous exponential decay: formula, 1 example, and its solution.
Formula
If a value shows
a continuous exponential change (growth or decay),
use this formula.
A = A0ert
A: Final value
A0: Initial value
e: Constant e
r: Rate of change (per time period)
t: Number of time period
Example
The initial value of the weight is 80g.
So A0 = 80g.
The weight decreases at a rate of 5% per minute.
So r = -0.05/minute.
Write the unit [per minute].
The final value is the weight 1 [hour] later.
But the unit of the rate is [per minute].
So write 1 hour in [minutes]:
t = 60 minutes.
A0 = 80
r = -0.05
t = 60
The weight decreases continuously.
Then the expected weight A is
A = 80⋅e-0.05⋅60.
-0.05⋅60 = -3
It says
assume e-3 = 0.05.
So 80⋅e-3 = 80⋅0.05.
80⋅0.05 = 4.0
The initial value A0 is in g.
So the final value A is 4.0g.
So 4.0g is the answer.