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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

Answer 1

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

In the event that P(n)=2*P(0), the population will have doubled after n years.

Then #2=e^(k*t)#

t = years k = annual population growth rate (currently 0.04). It should be noted that there is no carrying capacity or limiting factor in this case.

Compute #2=e^(k*t)#

#ln 2=t*0.04#

#0.69314718/0.04 = t#

#t=17.33 years#

I want to emphasize once more that population growth is exponential and that there is no upper limit.

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Answer 2

Roman Acosta

The formula to calculate population growth rate is:

Population Growth Rate (%) = ((Population at End of Period - Population at Beginning of Period) / Population at Beginning of Period) * 100

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.