1. 1. An account with a balance of $1000 pays 3. 65% annual
1. An account with a balance of $1000 pays 3.65% annual interest compounded daily. What is the balance at the end of 1 year if no money is added to the principal?
ANSWER $
Think: What if this interest was compounded..
Every hour?
Every minute?
Every second?
Continuously?

2. EXAMPLE 1
Leonhard Euler
( )
Natural base “e”

3. (5 ) ( ) EXAMPLE 1 Simplify natural base expressions
Simplify the expression. a. e2 e5 =
e2 + 5 = e7 b. 12 e4 3 e3 =
e4 – 3 4 = 4e (5 ) c.
e –3x 2 = 52 (
e –3x ) 2 = 25
e –6x = 25
e6x

4. EXAMPLE 2
Evaluate natural base expressions
Use a calculator to evaluate the expression.
Expression
Keystrokes
Display a. e4
[ ] ex 4 b.
e –0.09
[ ] ex
0.09

5. GUIDED PRACTICE
for Examples 1 and 2
Simplify the expression. 1. e7 e4
e11
ANSWER 2. 2
e–3
6e5 12 e2
ANSWER 3. 24 e8 4 e5 6 e3
ANSWER

6. GUIDED PRACTICE
4. Simplify (ex e –3x)2. 1
e4x
ANSWER
5. Use a calculator to evaluate e –0.35. (Round to three decimal places.)
ANSWER
0.705