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.
You probably mean exponential, not expotential.
Exponent is a mathematical term, such as 5x5 is the same as 5 squared or 5 to the power of 2. That would be a little 2 printed just to the right of the 5.
Exponential growth would be a vast amount of growth that at least grows by 100% every time.
sparksfarmer
An exponential growth curve describes when something doubles every time it multiplies. If you have one stupid person and he divides in two, you have two stupid people. If those two stupid people multiply you gave 4 stupid people. If those 4 people (stupid people btw) multiply there are now 8 astound people. if this keeps going ans each stupid person multiplies itself you can see how stupid people gruw faster and faster as there are more if them.
Think about it. Say a plant sprouts, then you have a certain amount of cells in said plant. Each of those cells multiply in some amount of time. So, for example, after a week, you have twice the cells you had before. But if the cells divide at the same rate, the next week, you'll get a plant with 4 times the cells you had before because the cells that divided and creates new cells, will still divide and create more new cells just like the new cells will divide and make new cells. The old cells don't stop making new cells after the first generation.
This can be stated in different equivalent ways, for example:
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.
Unlimited resources
J
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.
A population growth curve shows the change in the size of a population over time. It typically consists of four phases: exponential growth, plateau, decline, and equilibrium. The curve is often represented by an S-shaped logistic curve, which shows the pattern of population growth leveling off as it reaches carrying capacity.
Even numbers, Equilateral triangle, Exponential growth curve...
You can write an exponential curve in the form:y = A e^(Bx) And also in the form: y = C D^x Where A, B, C, and D are constants, and "^" represents a power. Also, with exponential growth, the function will increase or decrease by the same factor in equal time intervals (for example, double every 1.3 years; triple every 2 months; etc.).