Answer:
Basic Relationship
We will use the equation below to derive all the other forms:
(1) log(NN0)=rt
Where:
N0 (initial population) = The population at time t = 0.
N (future population) = The population at time t.
r (rate) = The rate of population change as a function of t (a 1% increase is expressed as 0.01).
This variable is called the Malthusian Parameter.
In population studies, r is usually taken to mean births minus deaths.
t (time) = The amount of time required to produce a growth in population proportional to N/N0.
Source: Wolfram Math World: Population Growth
Derived Forms
Here are the forms of equation (1) in terms of each of its variables:
(2) N=N0e(rt) (future population)
(3) N0=Ne(−rt) (present population)
(4) t=log(NN0)r (time)
(5) r=log(NN0)t (rate)
Note that e in the above equations is the base of natural logarithms, and log(x) refers to the natural logarithm of x.
Doubling time
At the present world population growth rate of 1.1% per year (Population Growth), how long will it take to double the world's population?
The appropriate equation for this case is (4) above, with the following arguments:
t=log(NN0)r=log(21)0.011=63.243 (years)
This equation shows that it will take about 63 years to double the world's population. If this prediction is borne out, there will be 14 billion people on Earth in 2074 (based on the 2011 population of 7 billion).
Rate of Increase
How many more people join us each day?
The base equation for this case is (2) above:
N=N0e(rt)
But because we want the increase per day, we will use this form:
Nd=N0e(rt)−
