Lesson 6.2 The Natural Base e Learning Goal: (F.IF.C.7e, F.LE.B.5) I can graph exponential functions, showing intercepts and end behavior. I can interpret the parameters in an exponential function in terms of context. Essential Question: What is the natural base e? Homework Discussion

Group Consensus Use a graphing calculator to graph the following. Describe the end behavior of the function as x approaches

Natural Base e called the Euler number - named after mathematician Leonhard Euler an irrational number Simplifying Natural Base Expressions Simplify each expression. a. b. c. Simplify the expression. 1. 2. 3. Your Turn

Transformation of Natural Base Exponential Functions Graphing Natural Base Exponential Functions Growth or Decay? Transformation of Natural Base Exponential Functions What value will affect whether the function is growth or decay? Example: Determine if the function is growth or decay. Then graph the function. a. y = 3ex b. f (x) = e−0.5x Your Turn c. y = d. y = 4e−x e. f(x) = 2e2x

Continuously Compounded Interest A: amount in account after t years P: the initial amount deposited r: the annual interest rate t: the number of years Example: Modeling with Mathematics You and your friend each have 
accounts that earn annual interest 
compounded continuously. The 
balance A (in dollars) of your 
account after t years can be modeled 
by A = 4500e0.04t. The graph shows 
the balance of your friend’s account 
over time. Which account has a 
greater principal? Which has a 
greater balance after 10 years? You deposit $4250 in an account that earns 5% annual interest compounded continuously. Compare the balance after 10 years with the accounts in the above example. Your Turn

Practice to Strengthen Understanding Exit Question: What is the natural base e? Practice to Strengthen Understanding Hmwk #3 BI p307-308 #3-8, 13, 15-25odd,35, 36