Why It Matters: Exponential and Logarithmic Functions
Why learn about exponential and logarithmic functions?
Many sources credit Albert Einstein as saying, “Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it.” You probably already know this if you have ever invested in an account or taken out a loan. Interest is the amount added to the balance. The beauty, in the case of investing, is that once interest is earned, it also earns interest. This idea of interest earning interest is known as compound interest. (It isn’t quite as beautiful on money you owe.) Interest can be compounded over different time intervals. It might be compounded annually (once per year), or more often, such as semi-annually (twice per year), quarterly (four times per year), monthly (12 times per year), weekly (52 times per year), or daily (365 times per year). And then there is one more option—continuous compounding—which is the theoretical concept of adding interest in infinitesimally small increments. Although not actually possible, it provides the limit of compounding and is therefore a useful quantity in economics.
Suppose you inherit $10,000. You decide to invest in in an account paying 3% interest compounded continuously. How can you calculate the balance be in 5 years, 10 years, and 50 years? You’ll want to know, especially for retirement planning.
In this module, you will learn about the function you can evaluate to answer these questions. And you will discover how to make changes to the variables involved, such as time or initial investment, to alter your results.
Learning Objectives
Exponential Functions- Evaluate an exponential growth function with different bases
- Use a compound interest formula
- Write an exponential function
- Find an exponential function given a graph
- Use a graphing calculator to find an exponential function
- Find an exponential function that models continuous growth or decay
- Graph exponential functions, determine whether a graph represents exponential growth or decay
- Graph exponential functions using transformations.
- Convert from logarithmic to exponential form.
- Convert from exponential to logarithmic form.
- Evaluate common and natural logarithms.
- Identify the domain of a logarithmic function.
- Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote
- Identify why and how a logarithmic function is an inverse of an exponential function
Licenses & Attributions
CC licensed content, Original
- Why It Matters: Exponential and Logarithmic Functions. Authored by: Lumen Learning. License: CC BY: Attribution.
CC licensed content, Shared previously
- Piggy bank on dollar bills. Authored by: Pictures of Money. Located at: https://www.flickr.com/photos/pictures-of-money/17299241862/. License: CC BY: Attribution.
