Exponential Growth: Final Value

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

Formula

Formula

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 Growth: Final Value

Example

Example

Solution

The initial value of the population is 10,000.
So A0 = 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.

A0 = 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 1.0712 = 2.252.

So 10000⋅1.0712 = 10000⋅2.252.

10000⋅2.252 = 22520

So 22520 is the answer.