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What is Exponential Growth?
In mathematics and physics, exponential growth is a type of growth in which the proportional rate of increase is proportional to the current size of the object. In other words, the size of the object is multiplied by the growth rate each time the object is measured. Exponential Growth – Explanation Graph Equation Decay .
For example, if an object is measured to be 2 centimeters long, and the growth rate is 1 centimeter per day, then the object will be 4 centimeters long after one day, 8 centimeters long after two days, and so on.
Exponential Growth Graph
The exponential growth graph is a graphical representation of how a quantity or population is growing over time. The x-axis represents time, while the y-axis represents the quantity or population. The graph will typically show a linear growth at the beginning, followed by an exponential growth.
Exponential Growth Equation
The exponential growth equation is a mathematical equation that models the growth of a population or other quantity that increases at a constant rate. The equation is
\[N=N_0e^{rt}\]
where
N is the population or quantity at time t
N 0 is the initial population or quantity
r is the growth rate
t is the time in years
Exponential Decay
In exponential decay, the decay rate is proportional to the current amount of the substance.
$\frac{dN}{dt} = k N$
Where
$dN$ = the change in the amount of the substance over time, in units of the substance
$dt$ = the change in time, in units of time
$k$ = the decay rate, in units of the substance per unit time
Exponential Decay Formula
The exponential decay formula is a mathematical equation that describes the rate at which a quantity decays over time. The equation is:
- The quantity “N” represents the amount of the substance at time “t” and “k” is the decay constant.
- The decay constant is a measure of how quickly the substance decays and is typically expressed in units of inverse time (e.g. seconds-1).
