Continuous Exponential Growth: Final Value

How to find the final value of continuous exponential growth: formula, 1 example, and its solution.

Formula

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

Exponential Growth: Final Value

Example

Example

Solution

The initial value of the weight is 10g.
So A0 = 10g.

The weight increases at a rate of 3% per second.
So r = 0.03/second.

Write the unit [per second].

The final value is the weight 1 [minute] later.
But the unit of the rate is [per second].

So write 1 minute in [seconds]:
t = 60 seconds.

A0 = 10
r = 0.03
t = 60
The weight increases continuously.

Then the expected weight A is
A = 10⋅e0.03⋅60.

0.03⋅60 = 1.8

It says
assume e1.8 = 6.05.

So 10⋅e1.8 = 10⋅6.05.

10⋅6.05 = 60.5

The initial value A0 is in g.

So the final value A is 60.5g.

So 60.5g is the answer.