# What is the formula to calculate population growth/rate?

## How do I use the formula for this word problem: A small country that had 20 million people in 1990 has experienced exponential growth in population of 4% per year since then. Write an equation that models this situation and use your equation to determine when the population will double. I know my formula ends up being: P(n) = 20 x (1.04)^n

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#### Explanation

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#### Explanation:

I want someone to double check my answer

10
Aug 25, 2016

P(n)=P(0)e^(kt)

#### Explanation:

If P(n)=2*P(0) (n years later population will be double of the initial one).

Then $2 = {e}^{k \cdot t}$

t= years
k=population growth rate per year (which is 0.04)
Note that there is no limiting factor (or carrying capacity) in this situation.

Compute $2 = {e}^{k \cdot t}$

$\ln 2 = t \cdot 0.04$

$\frac{0.69314718}{0.04} = t$

$t = 17.33 y e a r s$

Again I underline there is no upper limiting factor. Population growth is exponential.

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