Mastering Exponential Functions: Graphing Growth and Decay

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 Warm-Up Exercises 2. • 5 23 ( – )2 x 2 3. • – 3 42 1 + y – = State the domain and range of the function 4. 3. + Evaluate the expression without using a calculator. 1. 5 2 –

7. Warm-Up Exercises Warm-Up Exercises 1 ANSWER 25 y ≤ 3 ANSWER 40 2. • 5 23 ( – )2 x 2 3. • ANSWER – – 192 3 42 1 + y – = State the domain and range of the function 4. 3. + domain: all real numbers; range: ANSWER Evaluate the expression without using a calculator. 1. 5 2 –

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

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

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

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

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

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

23. Example 2 = 1 1 1 8 2 4 x 0 1 2 3 > b 1 y 1 2 1 – Graph when and y ab x a 1 = b. Make a table of values. Then plot the points. Draw a curve that passes through the plotted points, as shown at the right.

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

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

32. EXIT SLIP

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

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

35. 3. Evaluate the model when ( )x x M 1.3 42.5 7. = = ANSWER 266.68

36. Practice

37. Math is Fun.