Exponential and logarithmic functions are used to model a variety of real-world situations mainly related to finance, science, and population

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Exponential and logarithmic functions are used to model a variety of real-world situations mainly related to finance, science, and population. The amount of money in a bank account after a set number of years is modeled by an exponential function. Population growth and decay is modeled by an exponential function. The magnitude of an earthquake is determined using a logarithmic function. Respond to the following questions.

  • To what extent does mathematics model real life? 
  • Is there always a function that can be used to model the behavior of data? 
  • How can we use math to describe the world and make predictions? 
  • Were functions created to fit data, or did data just so happen to fit existing functions?