1. Date: Lesson 8.1

3. I can graph exponential growth functions; graph exponential decay functions. Common Core: CC.9-12.F.IF.7e CRS: FUN 501.

4. Topic: Exponential Growth. CC.9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.* CRS FUN 501. Evaluate polynomial functions, expressed in function notation, at integer values

5. Bell Ringer

6. Warm-Up Exercises Evaluate the expression without using a calculator. 5 2 3 2. State the domain and range of the function –y = ( 2 x – )2)2 3. + 4. 1. 5 2 – 3. – 3 4 2 1 +

7. Warm-Up Exercises Evaluate the expression without using a calculator. ANSWER 1 25 ANSWER 40 5 2 3 2. ANSWER – 192 State the domain and range of the function –y = ( 2 x – )2)2 3. + 4. ANSWER domain: all real numbers; range: y 3 ≤ 1. 5 2 – 3. – 3 4 2 1 +

17. Example 1 Graph when and Graph the function ab x y = 1a = 1b > 2x.2x. y = Make a table of values for the function. SOLUTION y 123 x 2 – 1 – 0

18. Example 1 Graph when and Graph the function ab x y = 1a = 1b > 2x.2x. y = Make a table of values for the function. SOLUTION y 1 2 2 4 3 8 x 2 – 1 – 4 1 2 1 1 0

19. Example 1 Graph when and Graph the function ab x y = 1a = 1b > 2x.2x. y = Make a table of values for the function. SOLUTION y 1 2 2 4 3 8 x 2 – 1 – 4 1 2 1 1 0 Plot the points from the table.

20. Example 1 Graph when and Graph the function ab x y = 1a = 1b > 2x.2x. y = Make a table of values for the function. SOLUTION y 1 2 2 4 3 8 x 2 – 1 – 4 1 2 1 1 0 Plot the points from the table. Draw a curve that passes through the plotted points, as shown.

21. Example 1 Graph when and Graph the function ab x y = 1a = 1b > 2x.2x. y = Make a table of values for the function. SOLUTION y 1 2 2 4 3 8 x 2 – 1 – 4 1 2 1 1 0 Plot the points from the table. Draw a curve that passes through the plotted points, as shown.

22. Example 2 Graph when and a. Graph ab x y = 1a 1b > = 3x.3x. y = 2 b. Graph 2x.2x. y = 4 1 Draw a curve that passes through the plotted points, as shown at the right. SOLUTION a. Make a table of values. Then plot the points. y 0 2 1 6 x 3 – 2 – 9 2 1 – 27 2 3 2

23. Example 2 b. Make a table of values. Then plot the points. y 2 1 3 2 x 1 – 4 1 2 1 10 8 1 Graph when and ab x y = 1a 1b > Draw a curve that passes through the plotted points, as shown at the right. =

24. Checkpoint 1. Graph the exponential function. Graph when ab x y = 1b > 4x4x y = 2. 5x5x y = ANSWER

25. Checkpoint 3. Graph the exponential function. Graph when ab x y = 1b > 3x3x y = 4 4. 2x2x y = 0.1 ANSWER

32. EXIT SLIP

33. Graph. Describe the asymptote and state the domain and range. 1. 2 3 2x2x y = The asymptote is the x -axis; domain: all real numbers; range: y > 0 ANSWER

34. y = 1 – > y 1 – The asymptote is the line ; domain: all real numbers; range: 2. Graph Describe the asymptote and state the domain and range. y = 3 1 2 x 2 – –.

35. ANSWER 266.68 3.Evaluate the model when M = 42.5 ( )x)x 1.3 = x 7.7.

36. Practice

37. Math is Fun.