1. Exponential Functions Learning Objective: to explore the graphs of exponential functions and the natural base. Warm-up (IN) 1.Complete the table. 2.Do the values in the table appear to be approaching a fixed decimal number? If so, what is the number rounded to three decimal places? 2.705 2.717 2.718

2. Notes! General exponential function EX 1 – graph -3 -2 0 1 2 3 x y -3 -2 0 1 2 3 x y

3. Basic Properties of the graph of f(x) = a x 1) All graphs go through (0, 1) 2) All graphs are continuous curves 3) The x-axis is a horizontal asymptote 4) If a > 1, then the function increases as x increases 5) If 0 < a < 1, then the function decreases as x increases

4. Ex 2 - Graph y = 4 x from [-3, 3] When are exponential functions used in the "real" world? money growth problems (compound interest) growth of populations (people, animals, bacteria, etc.) radioactive decay x y

5. Properties of Exponents! Remember It approaches 2.71828… We call it the number e It was discovered by Leonhard Euler, and it’s irrational just like Worksheet!

6. Ex 3 - Graph f(x) = 5e x from [-2, 2] x y

7. HW – graphing exponential functions wksht Out – Graph y = (1/3) x from [-3, 3] Summary – Today I learned… Don’t forget about POW!!