Exponential Decay is the rate of decay with respect to time. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Exponential decreases start fast and get slower, hence the problem with radioactive waste hanging around for ages. True exponential increases and decreases occur whenever the rate of change of something is proportional to the thing itself. The rate of change of decay is given by

The **Exponential Decay Formula** is given by

Where,

t is the time taken,

N_{o} is the initial no of atoms present at time t = 0,

N(t) is the no of atoms present after time t,

$\lambda$ is the decay constant.

t is the time taken,

N

N(t) is the no of atoms present after time t,

$\lambda$ is the decay constant.

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Below are problems on exponential decay which may be helpful for you.

Initial atoms No = 1 gram,

No of atoms after time t, N(t) = 1 - 0.03 = 0.97 g.

Initial atoms N

No of atoms after time t N(t) = 1 - 0.01 = 0.99 g,

Time taken t = 50 s

$\lambda$ = $\frac{2.303}{t}$ log $\frac{N_{o}}{N_{t}}$

= $\frac{2.303}{50}$ log $\frac{1}{0.99}$

= 2.026 $\times$ 10