Logarithms and Exponential Functions
According to Abramson et al. (2017), logarithmic and exponential functions are used to calculate the interest earned on investments or savings. For instance, if the interest earned on an investment is compounded, exponential functions are used to calculate the yearly interest earned on the investment. If the initial investment is $100 and makes a 5% interest, then the investment will earn $5 in the first year. The following year’s interest will be based on $105 as the principal amount. The exponential function is also used to estimate population growth based on a constant relative growth constant. Logarithmic and exponential functions are also collectively used in carbon dating based on a constant negative rate of decay.
The real-life applications of exponential growth are relevant because exponential growth refers to growth based on a similar percentage over equal increments of the initial domain. The phrase ‘exponential growth’ is sometimes used to refer to rapid growth. However, in mathematical terms, it helps calculate growth based on compounded increments (Abramson et al., 2017). For instance, carbon dating is used to estimate radio-active decay over a million years. It is difficult to handle such estimations using linear growth; hence the exponential growth model comes in handy.
Logarithms and exponential functions are related. One of the relationships between the two functions is that logarithmic functions are inverses of exponential functions. For instance, the inverse of the exponential function y = ax is x = ay (Abramson et al., 2017). This shows that a logarithmic function can be easily reversed to become an exponential function and vice versa. Based on the relationship existing between logarithms and exponential functions, logarithms can be used to solve exponential statements.
References
Abramson, J. P., Openstax, & Rice University. (2017). College algebra. Samurai Media Limited.
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Logarithms and Exponential Functions
Respond to the following prompts in a minimum of 175 words:
Search the internet for real-world applications of logarithms or exponential functions.
Share the application you discovered with the class along with how it relates to logarithms or exponential functions. Be sure to cite the resource.
What is the relationship between exponentials and logarithms?
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