# Continuous Exponential Growth: Final Value

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

## Formula

If a value shows

a continuous exponential change (growth or decay),

use this formula.

A = A_{0}e^{rt}

A: Final value

A_{0}: 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 10g.

So A_{0} = 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.

A_{0} = 10

r = 0.03

t = 60

The weight increases continuously.

Then the expected weight A is

A = 10⋅e^{0.03⋅60}.

0.03⋅60 = 1.8

It says

assume e^{1.8} = 6.05.

So 10⋅e^{1.8} = 10⋅6.05.

10⋅6.05 = 60.5

The initial value A_{0} is in g.

So the final value A is 60.5g.

So 60.5g is the answer.