The formula for exponential decay is:

y = a(1 - b)^{x}

where

y = the final amount

a = the original amount

b = the percentage change as a decimal, so 1 + b is the decay factor

x = time

**Example**

The coal stock at a mine decreases by 20% each year. There are currently about 5 million tons left at the mine. How much coal will be left in 10 years' time?

**Answer**

a = 5000000

b = 20% = 0.20 = 0.2

x = 10

y = a(1 - b)^{x} = 5000000 (0.8)^{10} = 536871

There will be roughly **537000 tons.**