1. Warm Up:

2. 6.2 Notes: The Natural Base “e”

3. The Basics  The natural base’s symbol is “e,” and is an irrational number (similar to pi). It is approximately 2.7183. You can find this on your calculator.  The graph for the natural base is the same shape as the exponential growth graphs (b > 1), with the same go-to point and asymptote.

4. Simplifying Natural Base Expressions:  Follow the same exponent rules we learned last semester.  Multiply = add exponents, divide = subtract exponents,  Exponent with exponent = multiply exponents  1) e 3 ∙ e 6 2) 3) (3e -4x ) 2

5. Graphing:  General function form: y = ae rx  When r > 0, the function is growth  When r < 0, the function is decay  Still use at least 3 points!  1) y = 3e x 2) f(x) = e -0.5x

6. Continuously Compounded Interest  We have a formula for when something is compounded continuously: A = Pe rt (The PERT formula – wash that math right out of your hair )  A is amount in your account after a period of time.  P is the amount you started with/deposited (called the principal)  r is the interest rate in decimal form  t is the amount of time it has been compounded for.

7. Example:  You deposit $4500 into your account, which is compounded continuously at 4%. How much will you have after 10 years?  You deposit $4250 into your account, compounded continuously at 5%. What is your balance after 6 years?

8. HW: p. 307 #3 - 26