2. Applications of Logs and Exponentials Section 3-4

3. Objectives I can solve interest rate problems using a calculator I can solve exponential growth and decay application problems

4. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Compound Interest After t years, the balance, A, in an account with principal P and annual interest rate r (in decimal form) is given by the following formulas:

5. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Compounding Terms (n) TermValue of (n) Annually1 Semi-annually2 Quarterly4 Monthly12 Daily365

6. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example Find the accumulated value of an investment of $8000 for 6 years at an interest rate of 6.85% if the money is compounded monthly.

7. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Your Turn Find the accumulated value of an investment of $4800 for 5 years at an interest rate of 3.85% if the money is compounded quarterly.

8. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example Find the accumulated value of an investment of $2000 for 8 years at an interest rate of 7% if the money is compounded continuously Solution: A= Pe rt A = 2000e (.07)(8) A = 2000 e (.56) A = 2000 * 1.75 A = $3501.35

9. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Your Turn Find the accumulated value of an investment of $3500 for 7 years at an interest rate of 5.5% if the money is compounded continuously

10. Application Problems

11. Many radioactive substances have a decay half-life. This is the time required for the radioactivity to decay away to ½ its original amount. “k” is the constant

12. Application Problems In almost all application problems, you will have to solve for “k” first Then you can solve for the required missing information

13. Application

14. Homework WS 6-5