Check Skills/Warm Ups Graph each function. 1. y = 3x 2. y = 4x 3. y = –2x Simplify each expression. 4. 32 5. 5–3 6. 2 • 34 7. 2 • 3–2 8. 3 • 2–1 9. 10 • 32

Solutions 1. y = 3x   2. y = 4x   3. y = –2x  4. 32 = 3 • 3 = 9 5. 5–3 = = = 6. 2 • 34 = 2 • (3 • 3 • 3 • 3) = 2 • 81 = 162 7. 2 • 3–2 = 2 • 1 3 2 = 2 3 2 = 𝟐 𝟗 3 • 2-1 = 3 • 1 2 1 = 𝟑 𝟐 or 𝟏 𝟏 𝟐 10 • 32 = 10 • (3 • 3) = 10 • 9 = 90 1 53 1 5 • 5 • 5 1 125

Homework Solutions 2. 1 32. − 27 8 20. 1  10–12 s 46. 𝑡 6 27 4. 0 2. 1 4. 0 6. 4 8. m3 10. y 12. 𝑡 11 27𝑚 4 14. 3  10–5 16. 4.2  103 7  10–3 20. 1  10–12 s 22. 1 𝑥 3 24. 81𝑎 4 16𝑏 4 26. 1 9 28. 8𝑝 3 125 30. 9 4 32. − 27 8 34. 8 𝑛 3 36. 1 43. 1 16𝑚 12 44. 1 25 45. 𝑎 6 46. 𝑡 6 27 52. 𝑎 4 4𝑏 10 53. 𝑎 5 𝑐 5 𝑏 3 56. 𝑟 5 𝑝 25 𝑞 5 59. 3𝑏 5 5𝑎

8-7: Exponential Functions Objectives: To evaluate exponential functions. To graph exponential functions.

Key Concepts: Exponential Function: a function that repeatedly multiplies an initial amount by the same positive number.

Example 1: Evaluate each exponential function. a. y = 3x for x = 2, 3, 4 x y = 3x y 2 32 = 9 9 3 33 = 27 27 4 34 = 81 81 b. p(q) = 3 • 4q for the domain {–2, 3} q p(q) = 3 • 4q p(q) –2 3 • 4–2 = 3 • = 1 16 3 3 3 • 43 = 3 • 64 = 192 192

Example 2: Suppose two mice live in a barn. If the number of mice quadruples every 3 months, how many mice will be in the barn after 2 years? ƒ(x) = 2 • 4x ƒ(x) = 2 • 48 In two years, there are 8 three-month time periods. ƒ(x) = 2 • 65,536 Simplify powers. ƒ(x) = 131,072 Simplify.

Try These: Evaluate each function rule for the given value. a.  y = 0.5x for x = 3 b.  ƒ(x) = 4 • 3x for x = –2 0.125 4 9

Example 3: Graph y = 2 • 3x. x y = 2 • 3x (x, y) –2 2 • 3–2 = = (–2, ) 2 2 • 32 = 2 • 9 = 18 (2, 18) x y = 2 • 3x (x, y) –2 2 • 3–2 = = (–2, ) 2 3 2 9 –1 2 • 3–1 = = (–1, ) 2 31 3 0 2 • 30 = 2 • 1 = 2 (0, 2) 1 2 • 31 = 2 • 3 = 6 (1, 6)

Example 4: The function ƒ(x) = 1.25x models the increase in size of an image being copied over and over at 125% on a photocopier. Graph the function. x ƒ(x) = 1.25x (x, ƒ(x)) 1 1.251 = 1.25 1.3 (1, 1.3) 2 1.252 = 1.5625 1.6 (2, 1.6) 5 1.255 = 3.0518 3.1 (5, 3.1) 4 1.254 = 2.4414 2.4 (4, 2.4) 3 1.253 = 1.9531 2.0 (3, 2.0)

Try These: Suppose an investment of $5000 doubles every 12 years. a.  How much is the investment worth after 24 years? b.  After 48 years? $20,000 $80,000 4. Graph y = –0.5 • 3x. 3. Graph y = 0.5 • 3x.

HW #42: p. 435 #1-10 (correct in class) Quiz 8B Tomorrow: 8.4, 8.5, 8.6 HW #43: p. 432 #1-18