1. Determine the value of the unknown. 5 min

2. WHAT DO EXPONENTIAL FUNCTIONS LOOK LIKE? Sec 3.1.1

3. For today’s lesson you will need: Graph paper Ruler Graphing calculator

4. Graph each on the same Grid

6. What the graphs have in common

7. Differences Different growth rates

8. What does Exponential Growth look like? x 2x2x2x2xy -3 2 -3 -2 2 -2 ¼ 2 -1 ½ 0 202020201 1 212121212 2 222222224 3 232323238 Consider y = 2 x Table of Values: Graph: Cool Fact: All exponential growth functions look like this!

9. Use a fresh grid; Graph each on the same Grid

11. What the graphs have in common

12. What does Exponential Decay look like? Consider y = (½) x Table of Values: x (½) x y -2 ½ -2 4 ½ -1 2 0 ½0½0½0½01 1 ½1½1½1½1½ 2 ½2½2½2½2¼ 3 ½3½3½3½31/8 Graph: Cool Fact: All exponential decay functions look like this!

13. How do the graphs in this column compare to the graphs in the next column?

14. Asymptotes One side of each of the graphs appears to flatten out into a horizontal line. An asymptote is a line that a graph approaches but never touches or intersects.

15. Asymptotes Notice that the left side of the graph gets really close to y = 0 as. We call the line y = 0 an asymptote of the graph. Think about why the curve will never take on a value of zero and will never be negative.

17. Homework Problems Read and take notes on Methods and Meanings on page 118. R & P Page 119 #7,8,10,13, 18-20