The description of why atoms decay is quite complicated involving quantum mechanics and nuclear physics. Value of a car or equipment that depreciates at a constant percent rate over time. Whenever something is decreasing or shrinking rapidly as a result of a constant rate of decay applied to it that thing is experiencing exponential decay.
In many ways you can think of it as the opposite of exponential growth.
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. So enamored are economists of growth that during recessions they often refer to negative growth. When politicians or economists chant their mantra -- we must GROW the economy -- they implicitly assume that our economy can grow exponentially into perpetuity. We can easily find an expression for the chance that a radioactive atom will survive be an original element atom to at least a time t.