G&R vwo C dl 3 9 Rij C. vo Schwartzbrg 1/10 1a A hoort bij rij IV; B hoort bij rij II; C hoort bij rij III D hoort bij rij I. 1b Bij rij I: 36, 49, 64; bij rij II: 8000, 16000, 3000; bij rij III: 17, 19, 1 bij rij IV: 4, 4, 4. a Tik i 6, vrvolgs 3 * µ - 10... J krijgt: u 6 = 734 u 8 = 6 566. b D twaalfd trm is u 11 = 177 15. c u 1 = 531 446 < 1 000 000 u 13 1 594 38 > 1 000 000 vaaf d 14 trm. 3ab Tik i 1000, vrvolgs 1.1 * µ - 50... u 3 = 1165,5 d zsd trm is u 5 = 1305,55. 3c u 7 1 474, 4 < 1500 u 8 1571, 8 > 1500 vaaf d gd trm. 4a Rij mt u 0 = 6 stds 4 rbij. Op d achtst rij zij u 7 = 54 zitplaats. 4b Rij mt u 0 = 6 stds 4 rbij. D twaalfd rij hft u 11 = 70 zitplaats. 5a u = u 1 + 5. 5b u = 3 u 1. 5c u = u 1 3. 5d u = u 1. 6a 1, 7, 19, 43, 91,... 6b u 7 = 763 < 1 500 u 8 = 1 531 > 1 500 vaaf d gd trm. 7a u = 3 + 4 u 1 mt u 0 = 8 gft u 5 = 9 15. 7b u = u 1 +,1 mt u 0 = 4 gft u 5 = 14, 5. 7c u = 5 + u 1 mt u 0 = 100 gft u 5 11, 97. 7d u = 1,3 u 1 mt u 0 = gft u 5 7, 43. 7 u = 10 + mt u = 1 + 1 0 3 gft u 5 4,01. u 8a u = u 1 + 3 mt u 0 = 48. 8b u 1 = u 1 mt u 0 = 0. 8c u = u 1 5 mt u 0 = 0. 9a D juist formul is u = 1, 04 u 1 100 mt u 0 = 1 000. 9b u13,39 u14 97,51 op 1-1-00 is r t wiig. 10a u = 1,06 u 1 50 mt u 0 = 1750. 10b Bij 1-1-019, dirct a ht opm, hoort u 1 677,85 ( ). 10c u14 905, 83 ( ) u15 3 030,18 ( ) op 1-1-0. 10d D rt va 007 dus 0, 06 1 750 = 105 ( ). 11a 11b Elk trm is d som va d tw voorafgaad trm. Omdat j d tw voorafgaad trm odig hbt. 11c D volgd acht: 13, 1, 34, 55, 89, 144, 33 377. 1a u = u 1 + 6 mt u 0 = is d rij, 8, 14, 0, 6,... 1b, 8, 14, 0, 6,... u = + 6. Dus a = 6. 1c u 1000 = + 6 1 000 = 6 00. 13a 13b 13c D 8 trm is u 7 = 7 + 7 = 49 + 14 = 63. 3 D 0 trm is v 19 = 19 3 19 + 1 = 6803. w = ( + 3)( ) = 500 ( = 0,1,,3,... TABLE) = w = 500. Dus d 3 trm.
G&R vwo C dl 3 9 Rij C. vo Schwartzbrg /10 14a u 5 = 15 + 6 = 1, u 6 = 1 + 7 = 8 u 7 = 8 + 8 = 36. 14b u = 1 + 1 1 + 1 = 35 ( = 0,1,,3,... TABLE) = 4 u 4 = 35. Dus 35 is ht 5 drihoksgtal. 14c u = 1 + 1 1 + 1 = 55 ( = 0, 1,, 3,... TABLE) u 30 = 496 u 31 = 58. Dus 55 is g drihoksgtal. 15a 6 rchthoksgtal is u 5 = 5 + 3 5 + = 4. 15b 5 vijfhoksgtal is v = 1 + 1 4 1 4 4 + 1 = 35. 15c Vor d formuls u = + + = 1 + 1 3 v 1 + 1 i op d GR. TABLE laat zi: u 14 = 40 v 14 = 330 = 14 gft v u = 90. 16a Vor d formul u = 0,5 + 1,5 + 1 i op d GR. TABLE u 0 = 1, u 1 = 3, u = 6, u 3 = 10, u 4 = 15 u 5 = 1. 16b D tid laag hft u 9 = 55 siaasappls. 16c Vor d formul v = 1 ( + 1)( + )( + 3) i op d GR. 6 TABLE gft v 9 = 0 stapl va 10 lag bstaat uit 0 siaasappls. 16d TABLE gft v 14 = 680 d stapl bstaat uit 15 lag. u 0 is d rst laag u 1 is d rst laag zovoort 0 + 1 + + 3 + 4 = + 3 0 + + 3 1 + + 3 + + 3 3 + + 3 4 = 40. 17 u u u u u ( ) ( ) ( ) ( ) ( ) 18a 18b 18c 19a 19b 19c 5 = u 0 + u 1 + u + u 3 + u 4 + u 5 = 7 + 9 + 11 + 13 + 15 + 17 = 7. 4 vi = v 0 + v 1 + v + v 3 + v 4 = 3 + 4 + 7 + 1 + 19 = 45. i = 0 4 wk = w 0 + w 1 + w + w 3 + w 4 = 1 + + 4 + 8 + 16 = 31. 3 = u 0 + u 1 + u + u 3 = 3 + 11 + 7 + 59 = 100. v j = v 0 + v 1 + v = 100 + 103 + 106, 09 = 309, 09. j = 0 5 wi = w 0 + w 1 + w + w 3 + w 4 + w 5 = + 1 + 1 + 1 = 1. i = 0 0a 0b 5 k + 7) = 7 + 10 + 13 + 16 + 19 + = 87. (3 4 (3i + i + 1) = 1 + 5 + 15 + 31 + 53 = 105. i = 0
G&R vwo C dl 3 9 Rij C. vo Schwartzbrg 3/10 1 rij I: vrschil stds 3; rij II: vrschil stds 0; rij III: vrschil stds mr; rij IV: vrschil stds 5; rij V: vrschil stds 1. Dus rij III hoort r it bij. a E rr mt u 0 = 18 v = 5 u = 18 + 5. b D 5 trm is u 4 = 18 + 5 4 = 338. c 18 + 5 = 498 (TABLE of 5 = 498) = 56. Dus u 56 = 498. Dit is d 57 trm. 3a Er is costat vrschil va 5 v = 5. 3b Rcursiv formul va dz rr: u = u 1 + 5 mt u 0 = 13; dirct formul va dz rr: u = 13 + 5. 3c D 38 trm is u 37 = 13 + 5 37 = 198. 3d u = 633 13 + 5 = 633 5 = 60 = 14. Dus u14 = 633. Dit is d 15 trm. 4a E rr mt u 0 = 1 03 v = 7 dirct formul: u = 1 03 7. u = 46 1 03 7 = 46 7 = 777 = 111. Dus u111 = 46. Dit is d 11 trm. 4b u > 0 1 03 7 > 0 7 > 1 03 < 146,14... 146. Dus 147 positiv trm. 5a E rr mt u 0 = 51 v = 4 dirct formul: u = 51 4. 5b D 1 trm is u 0 = 51 4 0 = 51 80 = 171. 5c u < 0 51 4 < 0 4 < 51 > 6, 75 63. Vaaf d 64 trm is u < 0. 6a E rr mt u 0 = 5 v = dirct formul: u = 5 +. 6bc u15 = 5 + 15 = 35; d 18 trm is u 17 = 5 + 17 = 39. 6d u = 60 5 + = 60 = 55 = 7,5. Dus vaaf u 8, dat vaaf rij 9. 7a (1 + + 3 +... + 99 + 100) = 100 101 1 + + 3 +... + 99 + 100 = 1 100 101. 7b 1 + + 3 +... + 48 + 49 + 50 50 + 49 + 48 +... + 3 + + 1 + 51 + 51 + 51 +... + 51 + 51 + 51 (50 kr ht gtal 51) Dus 1 + + 3 +... + 48 + 49 + 50 = 1 50 51 = 175. 8a 8b 5 u = 1 + = 1 k aatal trm ( u 0 u 5) 6 (18 + 5 5 + 18) = 093. 49 u = 1 + = 1 k aatal trm ( u 0 u 49) 50 (18 + 5 49 + 18) = 7 05. 9a E rr mt u 0 = 17 v = 4 dirct formul: u = 17 + 4. u = 149 17 + 4 = 149 4 = 13 = 33. 17 + 1 + 5 + 9 +... + 149 = 1 aatal trm (1 trm + laatst trm) = 1 34 (17 + 149) = 8. 9b E rr mt u 0 = 89 v = 6 dirct formul: u = 89 6. u = 17 89 6 = 17 6 = 7 = 1. 89 + 83 + 77 + 71 +... + 17 = 1 aatal trm (1 trm + laatst trm) = 1 13 (89 + 17) = 689. 30a 30b 8 (5 k + ) = 1 + = 1 0 8 + + = aatal trm ( u u ) 9 ( 5 8 ) 088. 100 (0,5 i + 0,8) = 1 + = 1 0 100 + + = aatal trm ( u u ) 101 (0,8 0,5 100 0,8) 605,8. i = 0
G&R vwo C dl 3 9 Rij C. vo Schwartzbrg 4/10 31a 4 u 1 1 = 3 + 4 is rr mt v = 3 = ( u 0 + u 4 = (4 + 3 4 + 4) = 1 000. 31b 0 u 1 1 = 6 + 11 is rr mt v = 6 (6 k + 11) = ( u 0 + u 0 = (11 + 6 0 + 11) = 1 491. 31c u = u 1 + 6 mt u 0 = 10 is rr mt v = 6 dirct formul: u = 6 + 10. 4 1 5 ( 1 = u 0 + u4) = 5 (10 + 6 4 + 10) = 050. 31d rr mt u 0 = 18 v = 3 dirct formul: u= 3 + 18. u = 81 3+ 18 = 81 3= 63 = 1. 1 1 ( 1 = u 0 + u 1) = (18 + 3 1 + 18) = 1089. 3 rr mt u 0 = 100 v = 3 dirct formul: u = 3 + 100. u > 0 3 + 100 > 0 3 > 100 < 33,3... 33 u 1 34 ( 1 k = u 0 + u 33) = 34 (100 3 33 + 100) = 1 717. 33 1 rr mt u 1 1 0 = 1 v = 4 dirct formul: u = 4 + 1 = ( u 0 + u 1 ) = (1 + 4 1 + 1) = 1188. 34a rr mt u 0 = 30, 6 v = 0,15 dirct formul: u = 0,15 + 30, 6. 4 1 5 ( 1 = u 0 + u4) = 5 (30, 6 + 0,15 4 + 30, 6) = 810,5 Eidtijd: 13 mi. 30,5 sc. 34b rr mt u 0 = 35, 76 v = 0, dirct formul: u = 0, + 35, 76. 4 1 5 ( 1 = u 0 + u 4) = 5 (35, 76 0, 4 + 35, 76) = 88 Eidtijd: 13 mi. 48 sc. 35a rr mt u 0 = 5 v = dirct formul: u = 5 +. 33 u = 1 + = 1 k 34 ( u 0 u 33) 34 (5 + 5 + 33) = 19 (zitplaats i sctor i d birig). 35b 1 sctor i d birig birig hft 1 19 = 15 504 zitplaats. D buitrig hft 1 13 = 6 006 zitplaats. Totaal zij r 15 504 + 6 006 = 1510 zitplaats ht aatal va 1 000 klopt wl. 35c D total ikomst zij 8 19 45 + 0,75 6006 15 = 53687,50 uro. 36a ( + 1) ( + 8) = + 8 + + 8 = + 10 + 8. 36b 1 ( + 1) ( 10) = 1 ( 10 + 10) = 1 ( 8 10) = 4 5. 36c ( + 1) ( + 8) = + 8 + + 8 = + 30 + 8. 36d 1 ( + 1) ( + 50) = 1 ( + 50 + + 50) = 1 ( + 5 + 50) = + 6 + 5. 37a 37b 38a 38b u = 1 + + = 1 + + + = 1 k ( 1) ( u 0 u ) ( 1) (1 4 1) ( + 1) (4 + 4 ). u > 1 k 500 ( + 1) (4 + 4 ) > 500 (TABLE of itrsct) 13. Dus vaaf = 13. ( k 8) = 1 + + = 1 + ( 1) ( 8 8) ( 1) ( 16). (3 k ) = 1 + + = 1 + = 1 + ( 1) (0 3 ) 3 ( 1) 1 ( 1).
G&R vwo C dl 3 9 Rij C. vo Schwartzbrg 5/10 39a u1 = 6 u 0 = 38 8v = 38 6 = 1 v= 1, 5 u 0 = u1 1v = 6 1 1, 5 = 8. D dirct formul is u = 8 + 1,5. 39b 39c 19 (8 + 1,5 ) = 1 + + = 0 (8 8 1,5 19) 445. u = + = 1 + + + = 1 k (8 1,5 ) ( 1) (8 8 1,5 ) ( + 1) (16 + 1,5 ). u > 1 k 100 ( + 1) (4 + 4 ) > 100 (TABLE of itrsct) 35. Dus vaaf = 35. 40a rr mt S 0 = 500 v = 1 dirct formul: S = 500 + 1. 40b S = 800 500+ 1 = 800 1= 300 = 5. Bij = 5 = 1 + 4 (dus 1 maad jaar a dcmbr 008) hoort jauari 011 (1 hoort bij jauari 009). 36 36 40c S = + = 1 k (500 1 ) + + = ( ) 37 (500 500 1 36) 100 49. 40d S = + = 1 + + + = 1 k (500 1 ) + + ( 1) (500 500 1 ) ( 1) (5 000 1 ). 40 1 ( + 1) (5000 + 1 ) > 1000 000 (TABLE of itrsct) 50. = 50 ( = 0 1 + 10) hoort bij oktobr 09 (1 hoort bij jauari 009 0 hoort bij oktobr 009). 41a rr mt u 0 = 5 v = 0, dirct formul: u = 5 + 0,. 41b u = 8,6 5 + 0, = 8,6 0, = 3,6 = 18, dit is i d 19 wk ( = 0 is i d 1 wk). 41c u = + = 1 + + + = 1 k (8,6 0, ) ( 1) (8,6 8,6 0, ) ( + 1) (17, + 0, ). 1 ( + 1) (17, + 0, ) > 50 (TABLE of itrsct) 31, dus vaaf wk 3. 4 rij I: ht quotiët va tw opvolgd trm is stds ; bij rij II is dat 1 bij IV is dat 1. 4 rij III: vrschil stds 1 mr. Dus rij III hoort r it bij. 43a Ht quotiët va tw opvolgd trm is stds 1,. 43b mr mt u 0 = 150 r = 1, dirct formul: u = 150 1,. 10 43c u 10 = 150 1, 7 740. 1 43d D 13 trm is u 1 = 150 1, 11145. 43 u > 15 000 150 1, > 15 000 (TABLE) 14. Dus vaaf = 14. 44a Omdat u = 1, 5 u 1 (ht quotit va tw opvolgd trm is 1,5). 44b mr mt u 0 = 500 r = 1,5 dirct formul: u = 500 1,5. 44c u > 100 000 500 1, 5 > 100 000 (TABLE) 14. Dus vaaf = 14. 45 E mr hft t mak mt xpotiël groi; rr hft t mak mt liair groi. 46a u mr mt u 0 = 00 = r = 0,5 dirct formul: u = 00 0,5. u 1 mr mt 0 36 dirct formul: 36. u u 46b u = = r = 1 u 1 = ( ) 1 46c rr mt u 0 = 50 u u 1 = v = 3, 5 dirct formul: u = 50 + 3, 5. 46d u 1 10 mr mt u 0 = 14 = r = = =,5 dirct formul: u 14,5. u 0,4 4 = 1
G&R vwo C dl 3 9 Rij C. vo Schwartzbrg 6/10 47a mr mt u 0 = 00 r = 1, 05 rcurs. formul: u = 1, 05 u 1 mt u 0 = 00 dir. formul: u = 00 1, 05. 47b u = 00 1,05 = 4 400 (TABLE) u 14 (1-1-01) < 4 400 u 15 (1-1-0) > 4 400. Dus i 01. 47c E rcursiv formul: u = u 1 1, 05 + 150 mt u 0 = 00. Tik i 00 da As 1,05 + 150 (op basisschrm) u 7 (1-1-014) < 4 400 u 8 (1-1-015) > 4 400. Dus i 014. 48a 15 aatal trm 16 k rst trm (1 factor ) 100 (1 1,1 ) ( 100 1,1 ) = = 3594, 97. 1 factor 1 1,1 14 15 00 (1 0,98 ) 48b v is mr mt v 0 = 00 r = 0, 98 vk = 614,31. 1 0,98 1 13 50 (1 1,45 ) 48c w is mr mt w 0 = 50 r = 1, 45 wk = 13806, 76. 1 1,45 49a mr mt u 0 = 11,3 r = 1, 074 dirct formul: u = 11,3 1, 074. 49b 1 1 13 k 11,3 (1 1,074 ) u k = ( 11,3 1,074 ) = 33,6 (miljard dollar). 1 1,074 50a mr mt u 0 = 8000 (1 jaar) r = 1,04 hft als dirct formul: u = 8000 1,04 50b 9 30 8 000 (1 1,04 ) u k = 1570 378 ( ). 1 1,04 51a D groi pr wk is mr mt u 0 = 5, (wk 1) r = 0, 8 dirct formul: u = 5, 0, 8. 7 D groi i d 8 wk is u 7 = 5, 0,8 1,1 (cm). Dus (ogvr) 11 mm. 51b 7 7 8 5, (1 0,8 ) ( k = ) = (cm) 1 0,8 51c 9 10 5, (1 0,8 ) + = + 1 0,8 5a 5b 53a 53b + 1 10 000 (1 0,6 ) 10 000 + 1 = = (1 0,6 ) = 5 000 (1 0,6 0,6 ) = 5000 15000 0,6. 1 0,6 0,4 > 4 999 5 000 15 000 0, 6 > 4 999 (TABLE) 19. Dus vaaf = 19. mr mt u 0 = 0 r = 1,1 dirct formul: u = 0 1,1. + 1 0 (1 1,1 ) + 1 = = 0 uk (1 1,1 ) = 00 (1 1,1 1,1 ) = 00 + 0 1,1. 1 1,1 0,1 u > 4 0 1,1 > 4. (TABLE) 8. Dus bij d 9 duurloop voor ht rst mr da 4 km. 8 8 9 k 0 (1 1,1 ) = ( 0 1,1 ) = 7 (km da totaal i zij 9 duurlop afglgd). 1 1,1 54a E mr mt H (0) = 7 00 r = 1, 03 dirct formul: H ( ) = 7 00 1, 03. 54b 10 Bij 004 hoort = 10 H (10) = 7 00 1, 03 9 866 (miljo kg). 11 11 ( ) = 700 1 1,03 700 (1 1,03 ) = (miljo kg) 1 1,03 103351. k 54c H ( ) + 1 700 (1 1,03 ) 54d H ( ) > 175 000 > 175 000 (TABLE) 18. Dus vaaf 01. 1 1,03
G&R vwo C dl 3 9 Rij C. vo Schwartzbrg 7/10 Diagostisch tots D1a u = 5 + 0 u 1 mt u 0 = 100 gft u 6 40 u 9 409. D1b u13 < 409, 9 u14 > 409, 9 vaaf d 15 trm. D1c Bladr door d tabl grswaard 409,939. Da u = 0, 75u 1 + 0 mt u 0 = 40. Db Bij 4 mi hoort = 3 u 3 = 6,875 (mg/litr). Dc Stug door lat rk grswaard is 6 (mg/litr). 3 D3a D3b D3c D4a D4b D4c D5a D5b D5c D 10 trm is u 9 = 9 4 9 = 16. D 30 trm is v 9 9 0 4 9 = = =. 9 + 6 35 7 3 w = 4 630 + 6 = 4 630 (TABLE) w 17 = 4 630. Dit is d 18 trm. 4 = u 0 + u 1 + u + u 3 + u 4 = 1 + 1 + 3 + 7 + 13 = 5. 3 vi = v 0 + v 1 + v + v 3 = 6 + 0 + 90 + 440 = 556. i = 0 5 (j + 1) = 1 + 3 + 9 + 19 + 33 + 51 = 116. j = 0 u = u 1 5 mt u 0 = 15 is rr mt v = 5 dirct formul u = 15 5. D 5 trm is u 4 = 15 5 4 = 3. u < 0 15 5 < 0 (TABLE of) 5 < 15 > 30,4 31. Dus vaaf d 3 trm is u gatif. 9 D6a u 1 1 = + 3 is rr = 30 ( u 0 + u9 ) = 30 (3 + 9 + 3) = 960. D6b rr mt u 0 = 18 v = 1 dirct formul: u= 1 + 18; u = 150 1+ 18 = 150 1= 13 = 11. 11 u = 1 + = 1 k 1 ( u 0 u11) 1 (18 + 1 11 + 18) = 1 008. 15 u = 4 + 5 is rr 4 k + 5 = 1 + = 1 0 + + = 16 ( u u ) 16 (5 4 15 5) 560. D6c ( ) u = 5 + 6 is rr u = 5 k + 6 = 1 + + = 1 + + + = 1 0 + + ( 1)( u u ) ( 1)(6 5 6) ( 1)(5 1). u = = 1 + + = 1 + + = 1 7 3 is rr 7 k 3 0 + ( 1)( u u ) ( 1)( 3 7 3) ( 1)(7 6). D7a k ( ) D7b ( ) u = 6 + 7 is rr 6k + 7 = 1 ( + 1)( u + = 1 + + + = 1 0 u + + ) ( 1)(7 6 7) ( 1)(6 14). 1 ( + 1)(6 + 14) > 1500 (TABLE of itrsct) 1. Dus vaaf = 1. D7c ( ) D8a E rr mt u 8 = 30 u14 = 45 6v = 15 v=,5 u 0 = 30 8, 5 = 10. D dirct formul is u = 10 +,5. D8b D som va d rst 40 trm is 1 40 ( u + = 1 0 u 39) 40 (10 + 10 +,5 39) = 350. D8c ( 10 +,5 k ) = 1 ( + 1)( u + = 1 + + + = 1 0 u + + ) ( 1)(10 10,5 ) ( 1)(,5 0). 1 ( + 1)(, 5 + 0) > 5 000 (TABLE of itrsct) 59. Dus vaaf = 59.
G&R vwo C dl 3 9 Rij C. vo Schwartzbrg 8/10 D9a mr mt u 0 = 800 r = 1,5 rcursiv formul: u = 1,5 u 1 mt u 0 = 800 dir. formul: u = 800 1,5. 0 19 D9b u0 u19 = 800 1,5 800 1,5 13878. 5 4 D9c u5 u4 = 800 1,5 800 1,5 435. D9d u > 500 000 800 1,5 > 500 000 (TABLE) 9. Dus vaaf d 30 trm. 9 10 100 (1 1,08 ) D10a mr 100 1,08 u = = 1 1,08 1448,66. 9 10 5 (1 4 ) D10b mr u = 5 4 u 9 = 1310 70 = = 1 747 65. 1 4 15 k D10c ( ) 16 50 (1 1,045 ) 50 1,045 = 1135,97. 1 1,045 D11a D11b + + (80 1,5 1 k ) 80 (1 1,5 = ) = 80 1 = = 1 1,5 0,5 (1 1,5 ) 160 (1 1,5 1,5 ) 40 1,5 160. + (10 1, ) 1 k 10 (1 1, ) = > (TABLE) = 1 1, 1 000 16. Dus vaaf 16.
G&R vwo C dl 3 9 Rij C. vo Schwartzbrg 9/10 Gmgd opgav 9. Rij G1a D rij u is rr mt bgitrm u 0 = 1 000 vrschil v = 3 dirct formul: u = 1 000 3. u 0 1 000 3 0 3 1 000 1000 = = = = 43, 5. Dus u 3 43 > 0 u 44 < 0. 43 u 1 44 ( 1 k = u 0 + u 43) = 5 (1000 + 1000 3 43) = 4. G1b D rij v is mr mt bgitrm v 0 = 1 000 factor r = 0, 96 dirct formul: v = 1 000 0, 96. v > 500 (TABLE) 16. 16 17 1000 (1 0,96 ) vk = 1510,33. 1 0,96 Ga D rij u is rr mt bgitrm u 0 = 300 vrschil v = 6. Dirct formul: u = 300 + 6 rcursiv formul: u = u 1 + 6 mt u 0 = 300. D rij v is mr mt bgitrm v 0 = 0,1 factor r =. Dirct formul: v = 0,1 rcursiv formul: v = v 1 mt v 0 = 0,1. Gb v > u (TABLE) 1. Dus vaaf = 1. Gc S 1 1 1 = = ( + 1) ( u 0 + u ) = ( + 1) (300 + 300 + 6 ) = ( + 1) (600 + 6 ). + 1 + 1 v0 (1 r ) 0,1 (1 ) + 1 T = vk = = = 0,1 (1 ). 1 r 1 + 1 T 0,1 (1 ) 1 > S > ( + 1) (600 + 6 ) (TABLE) 15. Dus vaaf = 15. G3a Rcursiv formul: u = 0, 9 u 1 + 500 mt u 0 = 10 000 (90% vrdampt it). G3b u 0 = 10 000 da 0,9 As + 500 gft u 8 = 715 u 9 = 6937. Dus a 9 dag. G3c Blijf op ENTER drukk. J krijgt d grswaard 5 000. Of 0,1 grswaard = 500 (vrdampt hovlhid = bijgvuld hovlhid) grswaard = 5 000. G4a Rcursiv formul: u = 1, 05 u 1 + 1 000 mt u 0 = 10 000. G4b Op 1 jauari 015 ( = 10) is ht saldo 8866, 84. u 0 = 10 000 da 1,05 As + 500 gft u10 8866,84. G4c u17 48 760,55 u18 5198,58. Dus op 1 jauari 005 + 18 = 03 is ht saldo voor ht rst mr da 50 000. G4d Rcursiv formul: u = 1, 05 u 1 5 000 mt op 1-1-03 u 0 = 5199 1 000 5 000 = 51199 5 000 = 46199. G4 u 1 3381,13 u 13 1 449, 81. u 1 hoort bij 1-1-03 hij ka 13 kr 5 000 opm. G4f Hij hft 10 000 + 17 1 000 = 7 000 uro gstort. Hij ka 13 5 000 + 3381 = 68381 uro opm. Dus 68381 7 000 = 41381 uro mr opgom da gstort. G5a Rcursiv formul: u = 1, 048 u 1 + 500 mt u 0 = 500. G5b Op 1 jauari 015 ( = 10) is ht saldo 7 09,61. u 0 = 500 da 1, 048 As + 500 gft u 10 7 09, 61. G5c Stug doorgaa gft: u 7 895 u 8 30153. Dus op 1 jauari 005 + 8 = 033 is voor ht rst mr da 30 000. 18 G6a Stl ht bdrag B ( ), da B 1, 04 = 10 000 B = 10000 4 936 ( ). 18 1,04 17 18 18 18 b (1 1,04 ) b (1 1,04 ) 100 b (1 1,04 ) 18 G6b E mr mt u 0 = b r = 1, 04 = = = = 5 b (1 1, 04 ). 1 1,04 0,04 4
G&R vwo C dl 3 9 Rij C. vo Schwartzbrg 10/10 G6c 17 18 18 1,04 b (1 1,04 ) 1,04 b (1 1,04 ) 18 E mr mt u 0 = b 1, 04 = 1, 04 b r = 1, 04 = = = 6 b(1 1, 04 ). 1 1,04 0,04 18 6 b(1 1, 04 ) = 10 000 b = 10000 374, 94 ( ). Z mot jaarlijks 375 ( ) stort. 18 6 (1 1,04 ) (totaal stort zij da ovr di 18 jaar 6750 uro) G7a Bij 5 dlmrs is d opbrgst 5 (000 5 10) = 43750 ( ). Bij 6 dlmrs is d opbrgst 6 (000 6 10) = 4540 ( ). Dit is 4540 uro mr. G7b R( ) = (000 10) = (000 10 ). G7c 1 + + 3 + 4 + 5 +... + = 1 (1 + ). 000 1 (1 + ) < 1 000 (TABLE) 45. Dus mists 45 dlmrs. G7d Bij 5 dlmrs is d prijs pr prsoo 569 + 53 = 6 ( ). D opbrgst is da 5 6 = 3344 ( ). Dat is 3344 30157 = 187 uro mr. G7 Vor T ( ) = (1950 0,5 ( + 1)) i op d GR. Opti maximum gft 50, 7 T 65 641 ( ). T ( ) is maximaal bij 51 dlmrs. G8a G8b G8c G8d D frqutis zij 1, 0, 11, 39, 75, 59, 3, 14, 8, 7, 5, 4, 3. Vor d lijst i op d GR mt STAT da Edit..,99. Dus gmiddld 6 rod. (i L 1 ht aatal rod i L d frqutis) 1-Var Stats L 1, L gft da x 5 1 1 1 T = tk = ( t 1 + t ) = (150 + 15 ) = (30 ) = 151. k = 1 T 30 60 = 1800 151 1800 (TABLE) 13. Dus Joris ka i 30 miut 13 volldig rod aflgg. 13 13 0,01 (1 ) bk = 81,91 d oudrs btal Joris da 81,91. 1 k = 1