# Exponential Growth: Final Value

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

## Formula

If a value shows exponential change (growth or decay),

use this formula.

A = A_{0}(1 + r)^{t}

A: Final value

A_{0}: Initial value

r: Rate of change (per time period)

t: Number of time period

## Example

The initial value of the population is 10,000.

So A_{0} = 10000.

The population increases at a rate of 7% per year.

So r = 0.07/year.

Write the unit [per year].

The final value is the value 12 [years] later.

And the unit of the rate is [per year].

So write 12 years in [years]:

t = 12 years.

A_{0} = 10000

r = 0.07

t = 12

So the expected population A is

A = 10000(1 + 0.07)^{12}.

(1 + 0.07) = 1.07

It says

assume 1.07^{12} = 2.252.

So 10000⋅1.07^{12} = 10000⋅2.252.

10000⋅2.252 = 22520

So 22520 is the answer.