Macao, Monaco, Singapore, Hong Kong and Gibraltar are the five most densely populated.

Two important measures of a population are population size, the number of individuals, and population density, the number of individuals per unit area or volume. Ecologists estimate the size and density of populations using quadrats and the mark-recapture method.

The most accurate way to determine population size is to simply count all of the individuals within the habitat.

Indirect observation

Population growth is based on four fundamental factors: birth rate, death rate, immigration, and emigration.

Population growth can be described with two models, based on the size of the population and necessary resources. These two types of growth are known as exponential growth and logistic growth.

And while every population pyramid is unique, most can be categorized into three prototypical shapes: expansive (young and growing), constrictive (elderly and shrinking), and stationary (little or no population growth). Let’s take a deeper dive into the trends these three shapes reveal about a population and its needs.

The three basic growth curves are constant exponential, and logistic growth. Exponential growth can be found in nature when a current population multiply.

Two modes of population growth. The Exponential curve (also known as a J-curve) occurs when there is no limit to population size. The Logistic curve (also known as an S-curve) shows the effect of a limiting factor (in this case the carrying capacity of the environment).

The J curve, or exponential growth curve, is one where the growth of the next period depends on the current period’s level and the increase is exponential. The S curve, or logistic growth curve, starts off like a J curve, with exponential growth rates.

The classic growth curve, as exemplified by a newly established bacterial colony, is divided into four phases, in order of their appearance: (1) lag phase; (2) log (logarithmic), or exponential, phase; (3) stationary phase; and (4) death, or decline, phase.

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Exponential growth produces a J-shaped curve, while logistic growth produces an S-shaped curve.

To calculate exponential growth, use the formula y(t) = a__ekt, where a is the value at the start, k is the rate of growth or decay, t is time and y(t) is the population’s value at time t.

From the given data, we can conclude the initial population value, x0, equals 10,000. Also, we have the growth rate of r = 5%. Therefore, the exponential growth formula we should use is: x(t) = 10,000 * (1 + 0.05)t = 10,000 * 1.05t .

How to calculate growth rate using the growth rate formula? The basic growth rate formula takes the current value and subtracts that from the previous value. Then, this difference is divided by the previous value and multiplied by 100 to get a percentage representation of the growth rate.

So, for example, this is how you would solve 6^3 without a calculator, from start to finish. Write: 6 6 6, because the base number is 6 and the exponent is 3. Then write: 6 x 6 x 6, to place multiplication signs between each of the base numbers. After that, multiply out the first multiplication sign, or 6 x 6 = 36.

What is 4 to the 2nd Power? The exponent of the number 4, 2, also called index or power, denotes how many times to multiply the base (4). Thus, we can answer what is 4 to the 2nd power as. 4 to the power of 2 = 42 = 16.

As the exponent is a positive integer, exponentiation means a repeated multiplication: 3 to the 2nd power = The exponent of the number 3, 2, also called index or power, denotes how many times to multiply the base (3). Thus, we can answer what is 3 to the 2nd power as. 3 to the power of 2 = 32 = 9.

36

Take exponents, for example, like writing 10 to the 2nd power. The first way to express 10 to the second power is to write two 10s with a multiplication sign in between, like this: 10 x 10. This indicates two factors (ie – second power) of 10 multiplied by itself.

100

10 to the power of 2 = 102 = 100. To stick with 10 to the power of 2 as an example, insert 10 for the base and enter 2 as the index, also known as exponent or power. 10 to the 2nd power is an exponentiation which belongs to the category powers of 10.

When a number is described as being to a ‘power,’ that is a signal to you that you’re going to be doing repeated multiplication. When a number is said to be to the ‘second power,’ this is also called ‘squared. ‘

103 is read as “10 to the third power” or “10 cubed.” It means 10 • 10 • 10, or 1,000. 82 is read as “8 to the second power” or “8 squared.” It means 8 • 8, or 64. The exponent applies only to the number that it is next to.