Exponential Growth: 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 Growth: Final Value

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.