About Exponential growth and decay formula
Exponential Growth And Decay
Exponential growth and decay refer to physical quantities that rapidly change in value or shape. The change can be measured using the exponential growth and exponential decay concepts, and the new obtained quantity can be calculated from the old one. Exponential growth and decay have the formulas f(x) = a(1 + r)t, f(x) = a(1 - r)t, respectively. Get the list of Maths Formulas.
What do you mean by Exponential Growth And Decay?
Quantities that fluctuate fast are subject to exponential growth and decay. The concept of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay refers to quantities that do not evolve in a linear fashion but rather in an exponential fashion.
The formula abx, where 'a' is the beginning quantity, 'b' is the growth factor, which is identical to the geometric progression's common ratio, and 'x' is the time steps for multiplying the growth factor, is the simplest expression of exponential growth and decay. The value of b for exponential growth is more than 1 (b > 1), while the value of b for exponential decay is less than 1 (b < 1).
Exponential growth is used to research bacterial growth, population growth, and money growth schemes, among other things. A rapid reduction in a quantity over time is referred to as exponential decay. Food decay, half-life, and radioactive decay may all be calculated using exponential decay.
The rate of growth is used as a factor in exponential growth. The r-value is anywhere between 0 and 1 (0 < r < 1). The growth factor can be defined as (1 + r). And 't' stands for the number of time steps required to multiply the growth factor. 't' can be either a whole number or a decimal number. The growth factor for exponential decay is (1 - r), which is less than 1.
Formulas of Exponential Growth And Decay
Exponential growth and decay have different interpretations of formulas which are interrelated and can be interpreted differently. The below table shows three different formulas for exponential growth and decay.
| Exponential Growth | Exponential Decay |
| f(x) is abx | f(x) is ab-x |
| f(x) is a(1 + r)t | f(x) is a(1 - r)t |
| P is Poet | P is Poe-kt |
In the above formulas 'a' or Po is the initial quantity of substance. Further for exponential growth b = 1 + r = ek and for exponential decay we have b = 1 - r = e-k.
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