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Homework

Homework. 1. (7.3). What is Natural Base e?. 1. Answer. Euler’s Number: 2.7138281. 2. (7.4 d1). What is a common logarithm?. 2 . Answer. A log with a base of 10. Written as log. 3. (7.4 D1). What is a natural logarithm?. 3 . Answer. A log with a base of e. Written as ln.

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Homework

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  1. Homework

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

  3. 1. Answer • Euler’s Number: 2.7138281

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

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

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

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

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

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

  10. 5. M(7.3) • What is the formula for Continuously Compounded Interest?

  11. 5 . Answer

  12. 6. M(7.5) • What is the formula for the Product Property?

  13. 6 . Answer

  14. 7. M(7.5) • What is the formula for the Quotient Property?

  15. 7 . Answer

  16. 8. M(7.5) • What is the formula for the Power Property?

  17. 8 . Answer

  18. 9. M(7.5) • What is the formula for Change of Base?

  19. 9 . Answer

  20. 10. M(7.) • What is the Exponential Growth Model?

  21. 10 . Answer

  22. 11. M(7.) • What is the Exponential Decay Model?

  23. 11 . Answer

  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 • 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 = $750.76

  28. 14. Solve(7.1-7.2) • How do you translate an exponential function when graphing?

  29. 14 . Answer • h = left & right (sign changes) • k = up & down

  30. 19. solve(7.4 D2) • Simplify the expression

  31. 15 . Answer • cancels out • 4x

  32. 16. Solve(7.4) • Rewrite the expression .

  33. 16 . Answer

  34. 17. Solve(7.4) • Find the inverse function of .

  35. 17 . Answer • Swap x & y. • X – 2 = • cancels out • y=

  36. 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: • Product Property • Quotient Property

  38. 19. Solve(7.6) • Solve the equation:

  39. 19 . Answer • Drop the • 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:

  41. 20 . Answer • Cancels out. • X = • Change of Base • X = 2.07

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

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

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

  45. 22 . Answer • , (2, 3) and (6, 12) • 12 = 3() • 4 = • b = • b = 1.26 • = 1.25 • y = 1.25

  46. bonus • Write an exponential growth function of the form 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.

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