Malthusian equation

The Malthusian equation, sometimes called the exponential law, describes exponential population growth and is of the form

where
P₀ - population size at time 0,
r - population growth rate (Malthusian population parameter)
t - time
P - population size at the end of t time periods.

A graph of population growth as a function of parameters and a description of the Malthusian growth model can be seen in the article Malthusian growth model. The calculator below allows you to find any of the above four parameters from the known three. Thus, you can get an answer to any of the following four questions:

1. What is the population size after t periods of time from an initial moment if the population at the initial moment is P₀ and the rate of increase is r?
2. What was the population size at the initial moment if it is known that after t periods of time from the initial moment, the population size is P and the rate of increase is r?
3. In what time will the population size reach the value P if the initial population size is equal to P₀ and the rate of increase is equal to r?
4. What would the population growth rate have to be to increase the initial population size P₀ to the value P in t periods?

Thus, for any Malthusian population model, you can calculate, for example, the time of doubling of the population at a given growth rate, and solve other similar problems. To do this, select what you want to find in the form below, fill in the three remaining values, and get the result.

Malthus equation

FindInitial population size Final population size Time Population growth rate

Initial population size

Final population size

Time (number of periods)

Population growth rate

Initial population size

 

Final population size

 

Time

 

Population growth rate

 

Calculate

Calculation precision

Digits after the decimal point: 2

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