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Decay Formula

Exponential problems usually move around the decay formula in mathematics. To show money, bacteria, fishes in a pond, the exponential growth or decay formula is used frequently. Where continuous growth or decay are shown in the form of small r and t is the time during which decay was measured. The decay formula can be compared to compound interest formula where interests are being compounded continuously.

Keep in mind that value of variables varies based on one equation to another but structure of formula always remains the same showing the equal relationship. Here is how to represent the decay formula in mathematics.

\[\ A = Pe^{rt}\]

\[\large N(t)=N_{0}\left ( \frac{1}{2}^{\frac{t}{t_{\frac{1}{2}}}} \right )\]

\[\large N(t)=N_{0}e^{\frac{-t}{r}}\]

\[\large N(t)=N_{0}e^-\lambda t\]

Where P is the initial amount, r is growth or decay rate, and t is the final time during which decay process was completed. As an example, think of atmospheric pressure around where pressure in the air decreases as you go higher. Exponential decay is common in physical processes like radioactive decay or cooling in a draft etc and they are represented by first order differential equation ahead. To simplify the calculations, take the logarithms or you can use calculators too for quick results. In mathematics, these are just the topics but in physics or chemistry, there are proper units dedicated to the exponential decay or growth formulas. So, it is used everywhere especially if you are interested in science or technical studies. So, basic understanding of this concept is necessary and a little practice will make you the pro.

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