Decay functions are used to model a data value that is decreasing over time. They are used commonly to monitor the population decline of colonies of animals in scientific studies. They are also used to model the decay and half-life of radioactive materials. There are many types of decay models, including linear, non-linear, quadratic and exponential. The linear model uses a constant rate of decay, and is the most simple decay function.

Familiarize yourself with the common form of the decay function: f(t) = C - r*t. In this equation, t is time, C is a constant, and r is the rate of decay.

Define the constant C. C is the starting value of the population. For example, if the study starts with 50 goats, then C is set to 50.

Define the constant r. r is the rate of decline. For example, if 2 goats die per year, then r is set to 2.

Insert the values of the variables to yield the final function: f(t) = 50 - 2*t. If this function is analyzed, it can be seen that the population will become extinct in 25 years.