Colloquial sense:
It's when the rate of growth is always increasing, rather than the rate of growth being constant.
Mathematical sense (a more exact definition):
It's when the rate of increase is directly proportional to the amount. This means that the amount will be multiplied by the same number over fixed periods of time.
For example, if you have ten thousand dollars in a bank account with a fixed interest rate (exponential growth) and the amount is currently increasing at a rate of one dollar per day, then when the money grows to fifteen thousand dollars it will be increasing at $1.50 per day. If your money takes ten years to triple from $200 to $600 then it will take another ten years for it to triple again to $1800.
exponential
Any time the RATE of increase is greater than one. For example : if a population were to double (note that 2 is greater than 1) each generation then it is referred to as exponential growth. Note also that there are now 7 billion people on Earth - exponential growth. What is "needed" for this kind of growth is an unlimited environment, since it does not exist in the real universe, exponential growth ALWAYS crashes.
In order to have exponential growth there must be sufficient resources to thrive. The problem with exponential growth is that since the world is finite at some point there will be overpopulation.
Exponential growth is when a population grows faster and faster and there is a population in explosion. This is unsustainable. The population will deplete and many will die. In Logistical growth the number of organisms are pretty much remained at a constant number of individuals.
the industrial revolution began
That would be an exponential decay curve or negative growth curve.
A curve
A J-shaped curve is often referred to as exponential growth, which illustrates a rapid increase in a population or entity over time. This curve demonstrates a steady rise and acceleration in growth without any limiting factors in place.
An exponential growth curve represents a pattern of growth where the rate of growth is proportional to the current size of the population or system. This leads to rapid and continuous acceleration in growth over time. Examples include bacterial growth in a petri dish or compound interest in finance.
The letter "J" is commonly used to refer to the characteristic shape of an exponential growth curve. This shape resembles the letter "J," as it starts off slowly, then accelerates rapidly as the population or quantity increases, reflecting the nature of exponential growth.
Unlimited resources
J
The formula for an exponential curve is generally expressed as ( y = a \cdot b^x ), where ( y ) is the output, ( a ) is a constant that represents the initial value, ( b ) is the base of the exponential (a positive real number), and ( x ) is the exponent or input variable. When ( b > 1 ), the curve shows exponential growth, while ( 0 < b < 1 ) indicates exponential decay. This type of curve is commonly used to model phenomena such as population growth, radioactive decay, and compound interest.
population growth begins to slow down
Logistic growth occurs when a population's growth rate decreases as it reaches its carrying capacity, resulting in an S-shaped curve. Exponential growth, on the other hand, shows constant growth rate over time, leading to a J-shaped curve with no limits to growth. Logistic growth is more realistic for populations with finite resources, while exponential growth is common in idealized situations.
A bacterial growth curve demonstrates the pattern of bacterial population growth over time. The curve typically includes lag phase (initial period of adjustment), exponential phase (rapid growth), stationary phase (growth plateaus as resources deplete), and death phase (population decline). Understanding these phases is crucial in studying microbiology, as they provide insights into how bacteria respond to environmental conditions.
Exponential growth is a rapid increase where the quantity doubles at a consistent rate. Real-life examples include population growth, spread of diseases, and compound interest. These graphs show a steep upward curve, indicating exponential growth.