# Notes on the Exponential Function: Growth and Decay : A Differential Equation

Many quantities that change over time demonstrate exponential growth or exponential decay. For example, populations grow exponentially as long as there are enough resources to carry the population as its numbers increase. Continually compounded bank balances grow exponentially at a rate that depends on the interest rate. On the other hand, radioactive materials tend to degrade over time; otherwise known as half-life. A characteristic that all of these natural processes possess is that their rate of change depends on the size…