1. The Natural Base, e Applications

2. The Formula for continuously compounded interest is:

3. A P r t Total amount Principal (amount invested) Interest rate time

4. Example 1 What is the total amount for an investment of $500 invested at 5.25% for 40 years and compounded continuously? A = $4083.08

5. Example 2 What is the total amount for an investment of $100 invested at 3.5% for 8 years and compounded continuously ? A = $132.31

6. The half-life of a substance is the time it takes for half of the substance to breakdown or convert to another substance during the process of decay. Natural decay is modeled by the function below.

7. N(t) k t The amount remaining Initial amount (at t=(0) Decay constant time

8. Example 3 Pluonium-239 has a half-life of 24,110 years. How long does it take for a 1 g sample of Pu-239 to decay to.1 g ? Step 1: Find decay constant ‘k’

9. Example 3--continued Pluonium-239 has a half-life of 24,110 years. How long does it take for a 1 g sample of Pu-239 to decay to.1 g ? Step 2: Solve for ‘t’ Pluonium takes approximately 80,229 years to decay.

10. Example 4 The half-life of carbon-14 is 5730 years. What is the age of a fossil that only has 8% of its original carbon-14? Step 1: Find decay constant ‘k’ Step 2: Solve for ‘t’ The age of the fossil is approximately 21,048 years.