1. Homework
𝒚=𝟎.𝟐𝟏𝟒𝒙 𝟐.𝟑𝟗
𝒚=𝟏.𝟗𝟑𝒙 𝟎.𝟖𝟒
𝒚=𝟏.𝟓𝒙 𝟏.𝟔𝟖
𝒚=𝟎.𝟖𝟏𝒙 𝟎.𝟑

2. 1. (7.3)
What is Natural Base e?

3. 1. Answer
Euler’s Number:

4. What is a common logarithm?
2. (7.4 d1)
What is a common logarithm?

5. A log with a base of 10. Written as log.
2 . Answer
A log with a base of 10. Written as log.

6. What is a natural logarithm?
3. (7.4 D1)
What is a natural logarithm?

7. A log with a base of e. Written as ln.
3 . Answer
A log with a base of e. Written as ln.

8. What is the formula for Compound Interest?
4. M (7.1 D3)
What is the formula for Compound Interest?

9. 4 . Answer
𝑨=𝑷(𝟏+ 𝒓 𝒏 ) 𝒏𝒕 A = amount after t years P = initial Principal (deposit) r = interest Rate t = time in years n = times per year

10. What is the formula for Continuously Compounded Interest?

11. 5 . Answer
𝑨=𝑷𝒆 𝒓𝒕

12. What is the formula for the Product Property?

13. 6 . Answer
𝒍𝒐𝒈 𝒃 𝒎𝒏= 𝒍𝒐𝒈 𝒃 𝒎+ 𝒍𝒐𝒈 𝒃 𝒏

14. What is the formula for the Quotient Property?

15. 7 . Answer
𝒍𝒐𝒈 𝒃 𝒎 𝒏 = 𝒍𝒐𝒈 𝒃 𝒎 − 𝒍𝒐𝒈 𝒃 𝒏

16. What is the formula for the Power Property?

17. 8 . Answer
𝒍𝒐𝒈 𝒃 𝒎 𝒏 =𝒏 𝒍𝒐𝒈 𝒃 𝒎

18. What is the formula for Change of Base?

19. 9 . Answer
𝒍𝒐𝒈 𝒄 𝒂= 𝒍𝒐𝒈 𝒃 𝒂 𝒍𝒐𝒈 𝒃 𝒄

20. What is the Exponential Growth Model?

21. 10 . Answer
𝑨=𝑷(𝟏+𝒓) 𝒕

22. What is the Exponential Decay Model?

23. 11 . Answer
𝑨=𝑷(𝟏−𝒓) 𝒕

24. 12.
How do you know if an exponential function is a growth or decay function?

25. 12 . Answer
You look at b in the equation 𝒚=𝒂𝒃 𝒙 . If 0 <b < 1, it is a decay function. If b > 1, it is a growth function.

26. 13. Solve (7.3)
You deposit $700 in an account that pays 3.5% annual interest compounded continuously. What is the balance after 2 years?

27. 13 . Answer
𝑨=𝑷𝒆 𝒓𝒕 𝑨=𝟕𝟎𝟎𝒆 𝟎.𝟎𝟑𝟓(𝟐) A = $750.76

28. How do you translate an exponential function when graphing?
14. Solve ( )
How do you translate an exponential function when graphing?

29. 𝒚=𝒂𝒃 𝒙−𝒉 +𝒌 h = left & right (sign changes) k = up & down
14 . Answer
𝒚=𝒂𝒃 𝒙−𝒉 +𝒌 h = left & right (sign changes) k = up & down

30. Simplify the expression 𝒍𝒐𝒈 𝟑 𝟖𝟏 𝒙 .
19. solve (7.4 D2)
Simplify the expression 𝒍𝒐𝒈 𝟑 𝟖𝟏 𝒙 .

31. 𝒍𝒐𝒈 𝟑 𝟖𝟏 𝒙 𝒍𝒐𝒈 𝟑 𝟑 𝟒 𝒙 𝒍𝒐𝒈 𝟑 𝟑 cancels out 4x
15 . Answer
𝒍𝒐𝒈 𝟑 𝟖𝟏 𝒙 𝒍𝒐𝒈 𝟑 𝟑 𝟒 𝒙 𝒍𝒐𝒈 𝟑 𝟑 cancels out 4x

32. Rewrite the expression 𝒍𝒐𝒈 𝟐 𝟑𝟐=𝟓.
16. Solve (7.4)
Rewrite the expression 𝒍𝒐𝒈 𝟐 𝟑𝟐=𝟓.

33. 16 . Answer
𝟐 𝟓 =𝟑𝟐

34. Find the inverse function of 𝒚=𝟒 𝒙 +𝟐.
17. Solve (7.4)
Find the inverse function of 𝒚=𝟒 𝒙 +𝟐.

35. 17 . Answer
𝒚=𝟒 𝒙 +𝟐 Swap x & y. 𝒙=𝟒 𝒚 +𝟐 X – 2 = 𝟒 𝒚 𝒍𝒐𝒈 𝟒 𝒙 −𝟐 = 𝒍𝒐𝒈 𝟒 𝟒 𝒚 𝒍𝒐𝒈 𝟒 𝟒 cancels out y= 𝒍𝒐𝒈 𝟒 𝒙 −𝟐

36. Condense the expression: y = 2log x + 3log y – 5log z
18. Solve (7.5)
Condense the expression: y = 2log x + 3log y – 5log z

37. 18 . Answer
y = 2log x + 3log y – 5log z Power Property: 𝒚= 𝒍𝒐𝒈 𝒙 𝟐 + 𝒍𝒐𝒈 𝒚 𝟑 − 𝒍𝒐𝒈 𝒛 𝟓 Product Property 𝒚=𝒍𝒐𝒈 𝒙 𝟐 𝒚 𝟑 −𝒍𝒐𝒈 𝒛 𝟓 Quotient Property 𝒍𝒐𝒈 𝒙 𝟐 𝒚 𝟑 𝒛 𝟓

38. Solve the equation: 𝒍𝒐𝒈 𝟓 𝒙 −𝟕 = 𝒍𝒐𝒈 𝟓 (𝟐𝒙 +𝟑)

39. 19 . Answer
𝒍𝒐𝒈 𝟓 𝒙 −𝟕 = 𝒍𝒐𝒈 𝟓 (𝟐𝒙 +𝟑) Drop the 𝒍𝒐𝒈 𝟓 x – 7 = 2x + 3 Subtract x from both sides. -7 = x + 3 Subtract 3 from both sides. -10 = x

40. 20. Solve (7.6)
Solve the equation: 𝟕 𝒙 =𝟓𝟔

41. 20 . Answer
𝟕 𝒙 =𝟓𝟔 𝒍𝒐𝒈 𝟕 𝟕 𝒙 = 𝒍𝒐𝒈 𝟕 𝟓𝟔 𝒍𝒐𝒈 𝟕 𝟕 Cancels out. X = 𝒍𝒐𝒈 𝟕 𝟓𝟔 Change of Base 𝒙= 𝒍𝒐𝒈 𝟓𝟔 𝒍𝒐𝒈 𝟕 X = 2.07

42. 21. Solve (7.7)
Write an exponential function in the form 𝑦=𝑎𝑏 𝑥 that passes through the points (3, 1) and (5, 4).

43. 21 . Answer
𝑦=𝑎𝑏 𝑥 , (3, 1) and (5, 4). 𝟏= 𝒂𝒃 𝟑 𝐚= 𝟏 𝒃 𝟑 𝟒= 𝒂𝒃 𝟓 𝟒= 𝟏 𝒃 𝟑 𝒃 𝟓 𝟒= 𝒃 𝟐 2 = b 𝒂= 𝟏 𝟐 𝟑 a = 1/8 𝒚= 𝟏 𝟖 (𝟐) 𝒙

44. 22. Solve (7.7)
Write a power function in the form 𝑦=𝑎𝒙 𝒃 that passes through the points (2, 3) and (6, 12).

45. 22 . Answer
𝑦=𝑎𝒙 𝒃 , (2, 3) and (6, 12) 𝟑=𝑎𝟐 𝒃 𝐚= 𝟑 𝟐 𝒃 𝟏𝟐=𝑎𝟔 𝒃 𝟏𝟐= 𝟑 𝟐 𝒃 ( 𝟔 𝒃 ) 12 = 3( 𝟑 𝒃 ) 4 = 𝟑 𝒃 𝒍𝒐𝒈 𝟑 𝟒= 𝒍𝒐𝒈 𝟑 𝟑 𝒃 b = 𝒍𝒐𝒈 𝟒 𝒍𝒐𝒈 𝟑 b = 1.26 𝒂= 𝟑 𝟐 𝟏.𝟐𝟔 = 1.25 y = 1.25 𝒙 𝟏.𝟐𝟔

46. bonus
Write an exponential growth function of the form 𝑦=𝑎𝑏 𝑥−ℎ +𝑘 whose graph has a y-intercept of 5 and an asymptote of 2.

47. bonus
Explain how you can determine if a power function is a good model for a set of data pairs.