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2013-03-11В В· Check-out how logarithmic and exponential functions can be applied to real life Exponential growth functions are often used to model population growth. Below is an interactive demonstration of the population growth of a species of rabbits whose population grows at 200% each year and demonstrates the power of exponential population growth. Selected Applications Exponential and logarithmic functions have many real life modeled by a logarithmic function. 1. Definitions: Exponential and Logarithmic Functions. by M. Bourne. Exponential Functions. Exponential functions have the form: f(x) = b^x where b is the base and x is the exponent (or power). If b is greater than 1, the function continuously increases in value as x increases.