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Applications of Exponential and Log Functions

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More Lessons for Intermediate Algebra
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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Videos, worksheets, and activities to help Algebra students.

In this lesson, we will learn

  • how to calculate compound interest (finite)
  • how to calculate compound interest (continuous)
  • how to solve exponential growth or decay word problems

The following tables give the Formulas for Simple Interest, Compound Interest, and Continuously Compounded Interest. Scroll down the page for more examples and solutions.
Interest Formulas

Compound Interest (Finite Number of Calculations)

One real world application of exponential equations is in compound interest. The formula for compound interest with a finite number of calculations is an exponential equation. We can solve for a parameter of this equation, and can use logarithms to access parameters in the exponent. Students may be asked to solve compound interest problems with interest compounded biannually, monthly, or daily. How to find the future value of an account that earns interest compounded monthly and continuously

Compound Interest (Continuously)

Problems that involve continuous compound interest use a different equation from problems that have finitely compounded interest, but the continuous compound interest equation is also an exponential equation. We use many of the same methods for calculating continuous compound interest as we do finitely compounded interest. To calculate compound interest, we can use logarithms and methods for solving exponential equations.

Continuously Compounded Interest

Exponential Growth and Decay

Exponential decay refers to an amount of substance decreasing exponentially. Exponential decay is a type of exponential function where instead of having a variable in the base of the function, it is in the exponent. Exponential decay and exponential growth are used in carbon dating and other real-life applications.

Learn how to solve an exponential growth or decay word problem This video shows how to solve the following word problem: A population is growing exponentially; there were 200 bacteria 3 days ago and 1000 bacteria yesterday. How many bacteria will be present tomorrow?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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