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Potenciando saberes

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POTENCIANDO SABERES
x < 3 ; y = -2x + 3 3 < x < 6 ; y = x - 3 ƒ(x) L1 b : intersección eje Y b = 3 y = m.x + b -3 = 3m + 3 -6 = 3m m = -2 y = -2x + 3 (3;-3) Ejercicio 1 L2 m = 3 – 1 = 2 = 1 6 – 4 2 y = m.x + b 1 = 4(1) + b b = -3 y = x -3 (4;1)
EJERCICIO 2 V (-2;3) h = -2 k = 3 y = a(x – h)2 + k 0 = a(-4 – -2)2 + 3 0 = 4a + 3 a = -3/4 y = -3(x + 2)2 + 3 4 (-4;0)
EJERCICIO 3 Cantidad : 60 - x Precio : 180 + 5x I = p.q I = (180 + 5x)(60 – x) = 10 800 + 120x – 5x2 = -5x2 + 120x + 10 800 a) h = -b 2a = -120 = 12 2(-5) P = 180 + 5(12) 240 b) I = 11 475 -5x2 + 120x + 10 800 = 11 475 -5x2 + 120x = 675 -5x2 + 120x – 675 = 0 CASIO x1 = 15 x2 = 9 C1 = 60 – 15 = 45 C2 = 60 – 9 = 51
EJERCICIO 4 ƒ(x) = a + b. ec.x asíntota a = 4 3 = a + b-e0 3 = 4 + b b = -1 0 = 4 – 1.e-5c e-5c = 4 Loge = -5c c = 0,28 A) B) E = c a + b -3 E = 1(0;3) (-5;0)
EJERCICIO 5 ƒ(x) = a + b. ec.x asíntota a = 4 3 = a + b-e0 3 = 4 + b b = -1 0 = 4 – 1.e-5c e-5c = 4 Loge = -5c c = 0,28 A) B) a + b + c 4 – 1 + 0,28 3,28
EJERCICIO 6 P(t) = 50. e0,02t a) P(0) = 50. e0,02(0) = 50 b) P(30) = 50.e0.03(30) = 91,1 c) 60 000 000 = 50 . e0,02t 1 200 000 = e0,02t Loge1 200 000 = 0,02 14 = 0,02 t = 700
EJERCICIO 7 S = 500 ( 4 – 3.e-0.1x ) a) S = 500 ( 4 – 3.e-0.1x ) S = 500 ( 4 – 3.e-0.1(0) ) S = 500 ( 4 – 3.1 ) S = 500 b) 1 200 = 500 ( 4 – 3.e-0.1x ) 12 = 5 ( 4 – 3.e-0.1x ) 12 = 20 - 15.e-0.1x 8 = 15.e-0.1x e-0.1x = 0,53 Loge0,53 = -0.1x x = 6.35
EJERCICIO 8 C = S/. 1 000 r = 7% t = 8 años a) F(t) = 1000(1 + 0.07)8 = 1 718 b) F(t)2 = 1000(1 + 0.07)8(4) 4 = 1 742 F(t) = C (1 + r)t c) F(t)3 = 1000(1 + 0.07)8(12) 12 = 1 748 d) F(t)4 = P.ert = 1000.e0.07(8) = 1 751
EJERCICIO 9 F(t) = C (1 + r)t a) 2C = C (1 + 0,12)12t 12 2 = 1,0112t Log1,012 = 12t 8.64 = 12t t = 7 b) 2C = C (1 + 0,12)t 2 = 1,12t Log1,122 = t t = 0,1 c) 2C = C.et.0,12 2 = et.0,12 Loge2 = 0,12t 0,69 = 0,12t t = 5,78 F(t) = C (1 + r)t.k k F(t) = C . et.r
EJERCICIO 10 “x” unidades x y 1 000 2 000 1 500 2 750 y = m.x + b m = 2 750 – 2 000 1 500 – 1 000 m = 750 = 1,5 500 2 000 = 1 000(1,5) + b b = 0,5 a) y = 1,5x + 0,5 y = 1,5(1 600) + 0,5 y = 2 400,5 b) 4 100 = 1,5x + 0,5 x = 2 733
EJERCICIO 11 P(t) = 8 000.e-0,12t a) 4 900 = 8 000.e-0,12t 0,61 = e-0,12t Loge0,61 = -0,12t t = 4,12 b) t = 0 P(t) = 8 000.e-0,12(0) = 8 000(1) = 8 000
EJERCICIO 12 P1 = 1 200 millones t = 10 años r = 15% anual Cap. mensual P2 = t = 5 años r = 12% anual Cap. continua a) F(t) = 1 200(1 + 0,15)10(12) 12 = 5 328 b) F(t) = 1 200.e5(0,12) = 2 186,5 c) F(t) = 1 200(1 + 0,15)5(12) + 1 200(1 + 0,12)5 (12) 12 12 = 2 528,6 + 2 180 = 4 708, 6 d) 2 528, 6 %12 = 210,7 2 180 % 12 = 181,67 -> 210,7 + 181,67 = 392,37

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Potenciando saberes

  • 2. x < 3 ; y = -2x + 3 3 < x < 6 ; y = x - 3 ƒ(x) L1 b : intersección eje Y b = 3 y = m.x + b -3 = 3m + 3 -6 = 3m m = -2 y = -2x + 3 (3;-3) Ejercicio 1 L2 m = 3 – 1 = 2 = 1 6 – 4 2 y = m.x + b 1 = 4(1) + b b = -3 y = x -3 (4;1)
  • 3. EJERCICIO 2 V (-2;3) h = -2 k = 3 y = a(x – h)2 + k 0 = a(-4 – -2)2 + 3 0 = 4a + 3 a = -3/4 y = -3(x + 2)2 + 3 4 (-4;0)
  • 4. EJERCICIO 3 Cantidad : 60 - x Precio : 180 + 5x I = p.q I = (180 + 5x)(60 – x) = 10 800 + 120x – 5x2 = -5x2 + 120x + 10 800 a) h = -b 2a = -120 = 12 2(-5) P = 180 + 5(12) 240 b) I = 11 475 -5x2 + 120x + 10 800 = 11 475 -5x2 + 120x = 675 -5x2 + 120x – 675 = 0 CASIO x1 = 15 x2 = 9 C1 = 60 – 15 = 45 C2 = 60 – 9 = 51
  • 5. EJERCICIO 4 ƒ(x) = a + b. ec.x asíntota a = 4 3 = a + b-e0 3 = 4 + b b = -1 0 = 4 – 1.e-5c e-5c = 4 Loge = -5c c = 0,28 A) B) E = c a + b -3 E = 1(0;3) (-5;0)
  • 6. EJERCICIO 5 ƒ(x) = a + b. ec.x asíntota a = 4 3 = a + b-e0 3 = 4 + b b = -1 0 = 4 – 1.e-5c e-5c = 4 Loge = -5c c = 0,28 A) B) a + b + c 4 – 1 + 0,28 3,28
  • 7. EJERCICIO 6 P(t) = 50. e0,02t a) P(0) = 50. e0,02(0) = 50 b) P(30) = 50.e0.03(30) = 91,1 c) 60 000 000 = 50 . e0,02t 1 200 000 = e0,02t Loge1 200 000 = 0,02 14 = 0,02 t = 700
  • 8. EJERCICIO 7 S = 500 ( 4 – 3.e-0.1x ) a) S = 500 ( 4 – 3.e-0.1x ) S = 500 ( 4 – 3.e-0.1(0) ) S = 500 ( 4 – 3.1 ) S = 500 b) 1 200 = 500 ( 4 – 3.e-0.1x ) 12 = 5 ( 4 – 3.e-0.1x ) 12 = 20 - 15.e-0.1x 8 = 15.e-0.1x e-0.1x = 0,53 Loge0,53 = -0.1x x = 6.35
  • 9. EJERCICIO 8 C = S/. 1 000 r = 7% t = 8 años a) F(t) = 1000(1 + 0.07)8 = 1 718 b) F(t)2 = 1000(1 + 0.07)8(4) 4 = 1 742 F(t) = C (1 + r)t c) F(t)3 = 1000(1 + 0.07)8(12) 12 = 1 748 d) F(t)4 = P.ert = 1000.e0.07(8) = 1 751
  • 10. EJERCICIO 9 F(t) = C (1 + r)t a) 2C = C (1 + 0,12)12t 12 2 = 1,0112t Log1,012 = 12t 8.64 = 12t t = 7 b) 2C = C (1 + 0,12)t 2 = 1,12t Log1,122 = t t = 0,1 c) 2C = C.et.0,12 2 = et.0,12 Loge2 = 0,12t 0,69 = 0,12t t = 5,78 F(t) = C (1 + r)t.k k F(t) = C . et.r
  • 11. EJERCICIO 10 “x” unidades x y 1 000 2 000 1 500 2 750 y = m.x + b m = 2 750 – 2 000 1 500 – 1 000 m = 750 = 1,5 500 2 000 = 1 000(1,5) + b b = 0,5 a) y = 1,5x + 0,5 y = 1,5(1 600) + 0,5 y = 2 400,5 b) 4 100 = 1,5x + 0,5 x = 2 733
  • 12. EJERCICIO 11 P(t) = 8 000.e-0,12t a) 4 900 = 8 000.e-0,12t 0,61 = e-0,12t Loge0,61 = -0,12t t = 4,12 b) t = 0 P(t) = 8 000.e-0,12(0) = 8 000(1) = 8 000
  • 13. EJERCICIO 12 P1 = 1 200 millones t = 10 años r = 15% anual Cap. mensual P2 = t = 5 años r = 12% anual Cap. continua a) F(t) = 1 200(1 + 0,15)10(12) 12 = 5 328 b) F(t) = 1 200.e5(0,12) = 2 186,5 c) F(t) = 1 200(1 + 0,15)5(12) + 1 200(1 + 0,12)5 (12) 12 12 = 2 528,6 + 2 180 = 4 708, 6 d) 2 528, 6 %12 = 210,7 2 180 % 12 = 181,67 -> 210,7 + 181,67 = 392,37