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
A logistic growth curve differs from an exponential growth curve primarily in its shape and underlying assumptions. While an exponential growth curve represents unrestricted growth, where populations increase continuously at a constant rate, a logistic growth curve accounts for environmental limitations and resources, leading to a slowdown as the population approaches carrying capacity. This results in an S-shaped curve, where growth accelerates initially and then decelerates as it levels off near the maximum sustainable population size. In contrast, the exponential curve continues to rise steeply without such constraints.
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.
The letter "J" is commonly used to refer to the characteristic shape of an exponential growth curve. This is because the graph of exponential growth resembles the letter "J," with a steep increase after a period of slower growth. The curve starts off slowly before rising sharply, reflecting how populations or quantities can grow rapidly under ideal conditions.
The J-curve typically refers to a type of growth pattern that resembles the letter "J," characterized by a rapid increase after an initial period of slow growth. This pattern can be associated with exponential growth when resources are unlimited, leading to a sharp upward curve. In contrast, logistic growth starts with a similar initial phase but eventually levels off as it approaches carrying capacity, resulting in an S-shaped curve. Therefore, the J-curve itself is more closely associated with exponential growth rather than logistic growth.
J
Unlimited resources
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