Things grow (or decay) exponentially when the time rate of change in the quantity is proportional to the amount of “stuff” already present. Thus, bacteria grow exponentially because the more you have,...Things grow (or decay) exponentially when the time rate of change in the quantity is proportional to the amount of “stuff” already present. Thus, bacteria grow exponentially because the more you have, the more they reproduce (until they run out of food, or their waste starts to poison the environment.) The decay of radioactive elements is exponential because as the number of radioactive atoms decreases, there are fewer available to decay, so less decay occurs.
