1. 6.6 The Natural Base, e Warm-up Learning Objective: To evaluate natural exponential and natural logarithmic functions and to model exponential growth and decay processes.

2. EX 1 – complete the table to investigate the growth of a $1 investment that earns 100% annual interest over one year. Compounding Schedule nValue, A Annually12.0000 Semiannually 22.2500 Quarterly 4 2.4414 Monthly 122.6130 Daily365 2.7146 Hourly87602.7181 Every minute5256002.7183 Every second 31536000 2.7183

3. e is called the natural base. It was discovered by Leonhard Euler, and it’s irrational just like EX 2 – Simplify EX 3 – use the calculator to evaluate : (round to 3 decimal places) Learning Objective: To evaluate natural exponential and natural logarithmic functions and to model exponential growth and decay processes.

4. e is used to find continuously compounded interest. Final amount Initial amount rate time the percent written as a decimal EX 4 – You deposit $1500 in an account that pays 7.5% annual interest compounded continuously. What is the balance after 3 years? Just e

5. Out – How long does it take an investment to double at an annual interest rate of 7.5% compounded continuously? Summary – I understand…