I'm a programmer and have a client who annually releases new products which have "long tail" type of sales curves, very heavy when initially released, tapering out until discontinued years later. He wants me to write some software that uses the historical sales to predict what the future demand for the product will be so he can keep proper inventory.
I'm almost positive there's some existing mathematics that will help me with this, but I'm too ignorant of what it might be to sufficiently google in order to learn it.
What branch of mathematics should I study in order to be able to solve my client's problem?