Exponential Decay Formula

About Exponential Decay Formula

Let us first define what exponential decay is before learning the exponential decay formula. In exponential decay, a quantity falls slowly at 1^st before rapidly decreasing. The exponential decay formula is used to calculate population decay (depreciation), & it can also be used to calculate half-life (the amount of time for the population to become half its size). Let's learn more about the exponential decay formula and look at several situations that have been solved.

What are Exponential Decay Formulas?

The exponential decay formula aids in determining the quick reduction over time, or exponential decrease. To calculate population decay, half-life, and radioactivity decay, the exponential decay formula is employed. The most common format is f(x) = a (1 - r)^x.

Where

a = initial amount

1 - r = decay factor

x = time period

1. f(x) = ab^x
2. f(x) = a(1-r)^t
3. P = P₀e^-kt

Here, b = 1 - r = e^-k

Exponential Decay Formula

The quantity drops gradually, followed by a quick decrease in the rate of change and growth over time. The exponential decay formula is used to calculate the reduction in growth. One of the following formulas can be used to calculate exponential decay:

f(x) = ab^x

f(x) = a(1-r)^x

P = P₀e^-kt

Where,

• a (or) P₀ = Initial amount
• b = decay factor
• r = Rate of decay (for exponential decay)
• x (or) t = time intervals (time can be in years, days, (or) months, whatever you are using should be consistent throughout the problem).
• k = constant of proportionality
• e- Euler's constant

Note: In exponential decay, always 0 < b < 1.Here, b = 1 - r ≈ e^-k.

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