Exponential Decay: Final Value

If a value shows exponential change (growth or decay),
use this formula.

A = A₀(1 + r)^t

A: Final value
A₀: Initial value
r: Rate of change (per time period)
t: Number of time period

Continuous Exponential Decay: Final Value

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

So the expected weight A is
A = 80(1 - 0.05)⁶⁰.

(1 - 0.05) = 0.95

It says
assume 0.95⁶⁰ = 0.046.

So 80⋅0.95⁶⁰ = 80⋅0.046.

80⋅0.046 = 3.68

The initial value A₀ is in g.

So the final value A is 3.68g.

So 3.68g is the answer.