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In this lesson, you will learn about the exponential function and how exponential growth is mathematically calculated. In addition, we will learn that exponential decay uses a very similar formula, so that once you understand how exponential growth works, you also understand how exponential decay works. For the exponential growth, we will discuss the doubling time, which is the amount of time it takes for the population to double. Similarly, for exponential decay we will consider the half life, which is the amount of time it takes for the population or sample to decay to half of its initial value. These equations come directly from the compound interest formula, which is also an exponential growth formula.