Exponential decay
F(x)= a^x, |a| < 1D: all realsR: y > 0X-int.: noneY-int.: (0,1)
Exponential decay is a mathematical process in which the magnitude of a quantity reduces exponentially over time. This process is characterized by a constant ratio of decrease over time. Exponential decay occurs when a quantity is reduced by a factor of the same value after equal time intervals.
The function that describes exponential decay is typically written as:
y = a * e ^ (-k * x)
where y is the final value of the quantity, a is the initial value of the quantity, e is a mathematical constant known as Euler’s number (~2.71828), k is a constant (known as the decay constant or rate of decay), and x is the time elapsed.
The rate of decay, k, determines the speed at which the quantity decreases over time. The greater the value of k, the faster the decay.
Exponential decay can be observed in many real-world situations, such as the decay of a radioactive substance or the dissipation of heat in an object. It is also commonly used in financial modelling, population studies, and other fields where the rate of decrease over time is of interest.
To calculate the value of a quantity after a given time using exponential decay, one can use the formula:
y = a * e ^ (-k * t)
where t is the time elapsed. This formula can be useful in predicting future values of a quantity, as well as in analyzing past data to determine the rate of decay.
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