 # There are abundant instances of practical applications of exponenti...

## Question

There are abundant instances of practical applications of exponential and logarithmic function in a wide variety of subject areas. From the logarithmic Richter scale function for measuring the magnitude of an earthquake or the logarithmic light intensity function to exponential functions modeling radioactive isotope decay or compounding interest continuously on an investment.

For this last discussion board use the Library or Internet to find a real-world application of either a logarithmic function or an exponential function. Try to find one that your classmates may not know about. (We are all trying to learn something new here!) Explain the meanings of all of the letter symbols in your chosen logarithmic or exponential function and explain what its purpose is.

Then, show your work for finding the inverse of your function. If your function is an exponential function then its inverse will be a logarithmic function with the SAME BASE; if your function is a logarithmic function then its inverse will be an exponential function with the same base. Finally, demonstrate that the two functions are inverses of each other using composition of functions similar to the processes shown in Section 3.7 and in Chapter 6 in our Abramson text.

## Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

Lactic acid bacteria present in curd tends to grow exponentially in number over time. The population of bacteria after a time t, can be modeled using the following equation:
P(t)= Poekt, where P0 is the initial population of the bacteria culture, t is the time elapsed and k denotes the exponential growth rate. This can also be modeled as a logarithmic function using the following steps:...

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