1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Evaluate natural exponential and natural logarithmic functions. Model exponential growth and decay processes. 6.6 The Natural Base, e

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms continuous compounding formula natural base natural exponential function natural logarithmic function 6.6 The Natural Base, e

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Continuous Compounding Formula 6.6 The Natural Base, e A: amount of the investment P: principal r: interest rate compounded continuously t: time A = Pe rt

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Evaluate exponential functions of base e and natural logarithms. 6.6 The Natural Base, e e 4.7  109.947 ln 6  1.7918 Use a calculator:

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Model exponential growth and decay processes by using base e. 6.6 The Natural Base, e An investment of $7400 at 12% interest is compounded continuously. How much will the investment be worth in 15 years? A = Pe rt = 7400e 0.12(15)  44,767.39 TOC