review 5 - exponents and logarithms - Review Question Exponential and Logarithmic Functions Multiple Choice L 10 IL The population of a bacteria colony

review 5 - exponents and logarithms - Review Question...

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Unformatted text preview: Review Question - Exponential and Logarithmic Functions Multiple Choice L 10 IL The population of a bacteria colony triples every hour. The initial population is 100. How many bacteria will there be in 5 hours? a. 500 c. 1500 b. @4300 d. 243x10” The population of a bacteria colony doubles every 20 min. If the initial population is 250, how many bacteria would there be in 3 hours? a. 128000 c. 512 b. 4500 d. 2000 The number of yeast cells in a culture grew exponentially from 200 to 6400 in 5 hours. What would be the number of cells in 10 hours? a. 128 000 c. 64 000 b. 12400 d. 204 800 The population of deer in a provincial park was 157 in 1990 and 351 in 1995. If the population continues to grow exponentially at this rate, what will it be in the year 2010? a. 3922 c. 933 b. 2451 d. 776 The frog population in a beaver pond declined exponentially from 1200 to 550 in 5 years. The growth rate for the frog population is: a. 2.18 c. 130 b. 0.458 d. 0.856 The value of an automobile decreases exponentially by 25% each year. About how much will a $35 000 car be worth in .9 years? a. $1335 c. $3500 b. $0 d. $2630 Which of the following statements is not true in describing the graph of an exponential function in the form )2 = ax, a > 0? a. The domain is the set of real numbers. b. The range is the set of positive real numbers. 6. The graph passes through the origin. d. y increases as x increases when a > 1. What is the equation of the asymptote to the function y = a x? a. x=1 0. 36:0 b. y=1 d- y=0 For the functiony= 3H, asx am: a. y—aw c. y—al b. y—a—oo d. yaE For the function y = a x, what happens if a = 0? a. The graph is a horizontal line through (0, l). b. The graph is a vertical line. 0. The function cannot be graphed. d. There is a ”hole" at the point (0, 0). For the equation y = a X, where a < 0: a. y is always decreasing b. y is always increasing 0. the graph is discontinuous as it contains "jumps" d. ' the graph is a straight line 12. 13. 14. 15. l6. l7. l8. 19. 20. 21. 22. 23. 24. The graph of y = C (tax + a" is related to the graph of 3! = (afby: a. a vertical stretch by factor 0 and a vertical shift by 0' units b. a vertical stretch by factor 6 and a horizontal shift by d units (3. a horizontal stretch by factor c and a vertical shift by d units (1. a vertical stretch by factor d and a vertical shift by 0 units The range of the function )2 = 5(2)Pf - 3 is: a. y < ——3 c. y > 5 b. y > ——3 d. y < 5 The y—intercept of the function )2 = 26:}: - 1 is: a. 2 c. 0 b. l d. -l The asymptote to the graph y = 3(2)x - 4 is: a. y = —4 c. y = *l b. y = 2 d. x = 2 The expression log381 = 4 written in exponential form is: a. 43 = 81 c. 813 = 4 b. 34 = 8 1 d. 381 = 4 Evaluate: lo g3 27’ a. 9 c 3 b. 18 d 2 1 Evaluate: 10132013) a. 4 C. —3 b. 3 d. —4 The equation y = 10g2 16 written in exponential form is: . 16 . a 2 = y c 2y = 15 . d. b 162 = y . ylfi = 2 Solve loggx = 3. a. 6 c. 9 b. 8 d. 5 Evaluate: 10g5 a}; a. 5 c. 0.5 b. l d. 2.5 Evaluate: log 100E] +10g100 a. log 1100 c. 100 000 b. 5 d. 2200 lo gain + legit: is equivalent to: a. 10 gafimn) 3- m 10 ga —- i2 13. lo gflfia + n) d. logfimfie) logax — 1:3ng is equivalent to: a. log.z (x — y) c‘ 10 Sa (5’0") 3” b. magi—x) , d0 loser—r] 25. 9:10ng is equivalent to: a. logaxy c. y‘logax b. logaxy d. logayx _.... '26. Evaluate: logfi + logZ a. 2.5 c. 1 b. log 2.5 d. log 7 _ 27. Evaluate: log3 243 — 10g381 a. 1 c. 3 b. 2 d. 4 W 28. Simplify: logafifi - loga40 a. logalé c. logalfil b. logfifi d. loga2240 it _ 29. Evaluate: logg32 7 a. 20 C- 20 7 . 35 b. 2.508 d- 16 7 _ 30. Evaluate: 103.2 + logfil + log432 a. 1 c. 4 b. 2 d. 8 _ 31. Express 2log4 -— 310g5+ 4logé as a single logarithm. a. log 12.8 c. log 1187 b. d. log 165.888 mgetgxiué) —4 32. Solve forx to two decimal places: 2: = 15 a. -0.09 c. 4.26 b. 11.5 d. 7.91 33. The change of base formula is: _ E 0. log y = logy x 10gb bay—ha t 1 bgy d. 10g}; Gaby: E3 10gby= E 34. Evaluate: 210g35 x 510g32 a. 6.47 C. 8.45 b. 10 d. 9.24 Short Answer 35. The mass of a radioactive substance decreases to half its value every 125 days. What would be the mass of a 500 g sample after 2 years? 36. What is the equation of the asymptote to the curve )2 = 3(2): — 2? 37. What is the y—intercept of the function )3 = 3(2):: — 4? 38. What transformation changes the graph of y = 3(2):: into 3: = 3(2)Fr — 4? 39. 40. 41. 42. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. What transformation changes the graph of y = (2): into y = 312)"? State the intercepts of the logarithmic function 3: = logax. What single transformation of the graph of y = ax would produce the graph of y = logflx? How are the exponential and logarithmic functions related? . Evaluate: lo g2 32 1 Evaluate: 10 g, 5 Evaluate: log, 9 3 Evaluate: lug3 IDS + log3 [g] Write 310352 — Zloga3 + 410g52 as a single logarithm in exact form. Solve for x: 310g: = log4125 Solve for x to two decimal places: 2: = 29 Solve forx to two decimal places: -8 x 22 = —'?9 5 Solve for x to two decimal places: 125 = 158”) Graph the function y = 3(2):; - 4 and state the domain, range, equation of the asymptote, and the y-intercept. 1 . Graph the function y‘ = (£31K + 3 and state the domain, range, equation of the asymptote, and the y—intercept. Without graphing, determine the domain, range, y-intercept, and equation of the asymptote of the function {(x) = 2(3)‘ + 7. Sketch the graph of y = 2x and Show how to use it to sketch the graph of )2 = log: it. Evaluate: 10g8 6 — 1th8 3 + log34 Solve for x: log, (x— l} — lug4 (x + 2) = 1 Solve for x: log3x +1th3 3 = log31 +10g34 The pH scale is a logarithmic scale for measuring the acidity of a chemical solution. It is calculated using pH = ~10 g[l—l+] , where [11+] is the molar concentration of hydrogen ions in the solution. If the pH of a solution changes from 2 to 8, by what factor does the hydrogen ion concentration change? A bacteria colony grows exponentially from 134 cells to 1241 in 24 hours. What is the doubling period in hours? Review Question - Eponential and Logarithmic Functions (Unit 6) Answer Section MULTIPLE CHOICE “H EQpWSQMP‘PNT‘ HHh—dHD—‘F—‘Hh—l .‘OSX’flQ‘EJ‘fi‘S’JN WMWWNNNNNNNNNN wwrcpwagwewwrp U.) P. UUJUUOD>OD>OUU>wOWOUOW>ww>OU>UOUU>U>Ufi SHORT ANSWER 36. y = — 37. (O, —1) 38. a vertical translation (shift) down 4 units 39. a vertical stretch by a factor 3 40. x—intercept: one, y-intercept: none 41. a reflection in the line y = x 42. They are inverses. 43. 5 44. —3 45. 1 46. 4 128 47. 1035 —9—— 48. 5 49. 4.86 50. 3.30 51. 1.63 52. Domain: 2: E R, Range: y > -4,y E R, Asymptote: y = —4, y—intercept: (0, —1) 53. Domain: 2: e R, Range: :1? :2 1,): E R, Asymptote: y = 3, y—intercept: (0, 6) 0 54. Domain: x e R, Range: y > 7, y-intercept (when x = 0): )7 = 2(3) + 7 = 9, asymptote: y = 7 55. As shown below, the graph of y = loggx is a reflection of the graph of )2 = 2K in the line y = x. 6x4 56. 10g36—10383+10g34=10g8 ~3— =10g88=1 x—l 57. logflx— 1)—-10g,,(x+ 2)=1 alog4[——~] =10g44 X+2 x—l —— =4—rzx—1=4x+8 ——>3x=~—9%x=—3 x+2 Since x > 1, there is no solution. 1x4 4 58. log3x+log33 =lug31+10g34 alag3x=10g3[———] -—>x=§ 3 59. pH = —10g[H+] ~—> 2 = —10g[H:] a H: = 10.2 = —1og[H;] —s~ 11;: 11]"3 H+ 10"3 Change factor: ——: = —~§ = 10—6 , H1 10 . 1 1 3.23.}. - _ — 1241 — 24 0g 134 so. M=C(2) ——:. 1241 = 134(2) —> ~— = 2 ~4— = — 134 D 10g2 2410g2 D: 1241 = 2.47 Ioglifi The doubling period is 7.5 hours. ...
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