Modeling Equations for Continuous Compounding and Solving for Time

This video tutorial covers solving for time in continuously compounding functions. It begins with an introduction to compounding interest, using examples of quarterly, monthly, and weekly compounding. The lesson then reviews solving exponential equations using logarithms, highlighting the differences between log base 10 and natural log. The concept of continuous compounding is explored, demonstrating how the expression approaches the irrational number e. Finally, practical applications are discussed, including calculating the future value of an investment with continuous compounding and determining the time needed to reach a financial goal.

What is the value of e in the context of continuous compounding?

How long will it take for an investment of $10,000 at 8% interest compounded continuously to reach $1,000,000?

What steps are involved in solving for time in a continuously compounding function?