Exponential functions and logarithmic functions occur in everyday life. Did you know that the Richter scale that measures the magnitude of earthquakes is based on the logarithmic scale?

Source: RichterFreqENergyGraph-en, Jkwchui, Wikimedia Commons

The Richter scale was created to measure and compare earthquakes occurring around the world. The value provides a reasonable reference point for waves recorded at teleseismic distances. For example, a 4 on a Richter scale means it is ten times more powerful than an earthquake with a magnitude of 3 and one tenth as powerful as an earthquake with a magnitude of 5. It would also mean that you could expect damage to poorly constructed buildings including broken windows and dishes.

An example of the use of an exponential function is the mosquito population. Have you ever wondered how to minimize the mosquito population?

After determining the exponential function for the growth of the mosquito population, you would then need to calculate the number of mosquitos there could be next week. If it rains, there could be more mosquitos, and if the weather is drier, there could be fewer mosquitos. Therefore, you'll need to make a reasonable conclusion and figure out a way to minimize the mosquito population.

In the following sections, you will find, interpret, and determine the reasonability of solutions to both exponential and logarithmic equations and inequalities.