
Population growth is basic to any environmental issue. Humans exert a profound physical impact on their immediate, regional and global environment.
 Space considerations
We take up space that was once forest, wetland, prairie or mountainside. While the space taken up by each individual varies. For example, it can be minimal such as in the cities of India or considerable such as in the late 1990 American singlefamily home which averages 2100 ft^{2} (0.05 acres or 0.02 hectares).
 Food considerations
We need to eat so land is required for agriculture. Much of that land is irrigated and fertilized with industrially produced fertilizers. Meat production produces animal wastes that can result in water pollution via runoff.
 Transportation
Roads cover permeable land with impervious paving and generate polluted runoff. They impact animals by dividing animals habitats which may accelerate species loss. Roads also provide human access to wilderness and forestland resulting in alterations of these areas.
 Waste Production
People in developed countries produce huge amounts of sewage as well as commercial, residential and industrial wastes. In the U.S. alone each individual produces about 725 Kg of municipal waste each year (exclusive of mining and other industrial waste.)
 Global considerations
An integrated world economy with loosely regulated world trade causes citizens of one country to seriously impact the environments of other countries. One country can obtain raw materials such as tropical hardwoods and ores from other countries. Toxins cross political boundries in the form of air and water pollution.
While each additional human being can contribute something, each places physical demands on the planet as well. Thus, the greater the world population the greater the demands on the environment. In addition, populations in developed countries consume disproportionaltely more resources than people in undeveloped countries.
The Mathematics of Population Growth
Exponential Growth
"Exponential growth, in general, is not understood by the lay public. If exponential use of a resource is not accounted for in planning  disaster can happen. Its not too great of simplification to state that the failure to understand the
concept of exponential growth by planners and/or legislators, is the single biggest problem in all of Resource Management." (Go here for more information. Scroll down the page to find the exponential growth information.)
When any quantity (rate of oil consumption, human population, your bank account) grows at a fixed rate or percentage each year such as 5% (contrast that to a fixed quantity such as $100) that growth is termed exponential. Exponential growth, such as population growth, is calculated using a compound interest formula (like that used to calculate interest in bank accounts.)
Calculating Exponential Growth (requires calculator with an exponent key)
 N = N_{0} (e)kt  
e = 2.71828
N = future value
N_{0} = present value
k = rate of increase
t = number of years over which
growth is to be measured

EXAMPLE 
Project the world population in 2017 given the 1997 midyear population of 5.85 billion and a growth rate of 1.36% per year
N = N_{0} (e)^{kt}
N = (5.85 x 10^{9}) x e^{(0.0136 x 20)}
N = 7.679 x 10^{9}
The population in 2017 will be 7.679 billion

Read more about population growth here.
Population Density
By modifying the compound interest formula, you can determine how long it would take for a given population at a particular growth rate to reach a density of one person per unit of earth's surface area.

t = (1/k)ln(N/N_{0}) 

t = time in years
k = growth rate
ln = natural log
N_{0} = starting population
N = population density 
EXAMPLE 
Starting with the 1997 population and using a world population growth rate of 1.36% determine in what year will the population density reach 1 person/ m^{2} on dry land. (The earth has a dry land area of 1.31 x 10^{14} m^{2}.)
t = (1/k)ln(N/N_{0})
t = (1/0.0136)ln[(1.31 x 10^{14})/( 5.85 x 10^{9})]
# years to reach 1.31 x 10^{14} persons = 736.5 yr
1997 + 736 = 2733
A population density of 1 person/m^{2} would be reached in the year 2733.

PROBLEMS 
 There are already places on earth where population densities approach the
1 person/m^{2} . A two story building in Delhi, India
was found to house 518 individuals (density of 1 person/ 1.5 m^{2}).
Calculate the floor area of the building in Delhi.
Compare this to the average floor area of the typical single family
home built in the U.S. in 1995 (2095 ft^{2}).
 The land area of Brooklyn, NY is 70.5 mi^{2} (1990 data). In 1992 the population of Brooklyn was 2,286 million. Calculate the population density of Brooklyn in terms of people per square meter.
(1 mi^{2} = 2.6 km^{2} )
 If the earth's population growth is 1.36% per year, in what year will the
world population reach the same density as Brooklyn's 1992 population
density? Is it likely that this density will ever be reached?

