%PDF-1.6
%
3 0 obj
<><><>]/ON[142 0 R]/Order[]/RBGroups[]>>/OCGs[142 0 R]>>/Pages 126 0 R/Type/Catalog>>
endobj
141 0 obj
<>/Font<>>>/Fields 146 0 R>>
endobj
127 0 obj
<>stream
2006-09-22T22:27:03
03. Ecuaciones logarítmicas y exponenciales - Microsoft Word
2024-02-22T23:22:44+01:00
2024-02-22T23:22:44+01:00
Acrobat PDFWriter 5.0 para Windows NT
application/pdf
uuid:6b8119db-ed7d-4d16-8988-3337d581e346
uuid:0cd4cced-4331-4243-92ab-12d51e148a7f
endstream
endobj
126 0 obj
<>
endobj
5 0 obj
<>
endobj
60 0 obj
<>
endobj
59 0 obj
<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Type/Page>>
endobj
64 0 obj
<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Type/Page>>
endobj
68 0 obj
<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Type/Page>>
endobj
72 0 obj
<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Type/Page>>
endobj
78 0 obj
<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Type/Page>>
endobj
82 0 obj
<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Type/Page>>
endobj
162 0 obj
<>stream
BT
0 0 0 rg
/TT0 9.96 Tf
0.05 Tc 51.24 762.12 Td
(21.)Tj
0.0149 Tc 0.3551 Tw 19.56 0 Td
(Un pueblo creci\363 en forma exponencial de 10.000 habitantes en 1980 a \
14.000 habitantes en 1990. Suponiendo que)Tj
0.0116 Tc 0.0276 Tw 0 -11.52 TD
(contin\372e el mismo ritmo de crecimiento, \277cu\341l ser\341 la poblac\
i\363n en el a\361o 2010?)Tj
/TT1 9.96 Tf
0.0087 Tc 0.6213 Tw 0 -11.64 TD
(La tasa de crecimiento)Tj
0.0276 Tc 0.6024 Tw ( actual es, aproxim)Tj
0.0244 Tc 0.6056 Tw 180.24 0 Td
(adamente, del 3\22242)Tj
0.03 Tc 0 Tw 84.84 0 Td
(1969)Tj
0.0124 Tc 0.5909 Tw ( %. Por tanto, la poblaci\363n en el a\361o 2010)Tj
0.0102 Tc 0.0198 Tw -265.08 -11.52 Td
(ser\341 de )Tj
0.035 Tc -0.005 Tw (27.440 )Tj
0.0034 Tc 0 Tw (habitantes.)Tj
/TT0 9.96 Tf
0.05 Tc -19.56 -16.32 Td
(22.)Tj
0.0156 Tc 1.0944 Tw 19.56 0 Td
(Un ordenador se deprecia de forma gradual a raz\363n del 25 % anual. Si \
hoy compramos un ordenador que cuesta)Tj
0.03 Tc -0.12 Tw 0 -11.52 TD
(2.000 )Tj
0.0153 Tc 0 Tw 25.08 0 Td
(euro)Tj
-0.0217 Tc (s:)Tj
0.0305 Tc -25.08 -11.4 Td
(a\))Tj
0 Tc 0.0706 Tw 14.28 0 Td
(\277Cu\341l ser\341 su valor dentro de 3 a\361os y medi)Tj
0.0389 Tc 0 Tw 174.48 0 Td
(o?)Tj
0.0517 Tc -188.76 -11.52 Td
(b\))Tj
0.0047 Tc 0.0424 Tw 14.28 0 Td
(\277Cu\341l ser\341 su valor dentro de 15 meses?)Tj
/TT1 9.96 Tf
0.0517 Tc 0 Tw -14.28 -11.76 Td
(a\))Tj
0.0558 Tc 14.16 0 Td
(730\222)Tj
0.06 Tc -0.03 Tw 18.36 0 Td
(71 )Tj
0 Tw (\200)Tj
-0.0472 Tc -32.52 -11.52 Td
(b\))Tj
0.0242 Tc -0.1142 Tw 14.16 0 Td
(1.395\22291 )Tj
0.06 Tc 0 Tw 38.4 0 Td
(\200)Tj
/TT0 9.96 Tf
0.05 Tc -72.12 -17.04 Td
(23.)Tj
0.0094 Tc 0.0406 Tw 19.56 0 Td
(Una poblaci\363n tiene una tasa de crecimiento anual del 2 %. Se pide:)Tj
0.0305 Tc 0 Tw 0 -11.4 TD
(a\))Tj
0.013 Tc 0.017 Tw 14.28 0 Td
(La funci\363n exponencial del crecimiento.)Tj
0.0517 Tc 0 Tw -14.28 -11.52 Td
(b\))Tj
0.0088 Tc 0.0305 Tw 14.28 0 Td
(Si se mantiene este ritmo de crecimiento, \277cu\341nto tiempo tardar\341\
en duplicarse la poblaci\363n?)Tj
/TT1 9.96 Tf
0.0517 Tc 0 Tw -14.28 -12.6 Td
(a\))Tj
/TT2 9.96 Tf
0.0344 Tc 14.16 0 Td
(P)Tj
/TT2 6.48 Tf
-0.0014 Tc 6.12 -1.56 Td
(t)Tj
/TT1 9.96 Tf
0 Tc 0.03 Tw 1.8 1.56 Td
( )Tj
/TT3 9.96 Tf
0.052 Tc 0 Tw (=)Tj
/TT1 9.96 Tf
0 Tc 0.03 Tw ( )Tj
/TT2 9.96 Tf
0.0344 Tc 0 Tw (P)Tj
/TT1 6.48 Tf
0 Tc 16.68 -1.56 Td
(0)Tj
/TT1 9.96 Tf
0.03 Tw 3.24 1.56 Td
( )Tj
/TT3 9.96 Tf
0.03 Tc 0 Tw 2.4 0 Td
(\327)Tj
/TT1 9.96 Tf
0.0258 Tc 0.0042 Tw 2.64 0 Td
( 1\22202)Tj
/TT2 6.48 Tf
-0.0014 Tc 0 Tw 20.88 4.56 Td
(t)Tj
/TT1 9.96 Tf
-0.0767 Tc -0.0133 Tw 1.8 -4.56 Td
( \()Tj
/TT2 9.96 Tf
-0.0089 Tc 0 Tw 5.76 0 Td
(t)Tj
/TT1 9.96 Tf
-0.0018 Tc 0.0318 Tw ( a\361os\))Tj
-0.0472 Tc 0 Tw -75.48 -11.4 Td
(b\))Tj
0.0706 Tc -0.0406 Tw 14.16 0 Td
(35 a\361)Tj
0.0728 Tc 0 Tw 23.16 0 Td
(os)Tj
/TT0 9.96 Tf
0.05 Tc -56.88 -17.04 Td
(24.)Tj
0.022 Tc 0.2732 Tw 19.56 0 Td
(Las tasas de inter\351s en los pr\351stamos se camuflan muchas veces pon\
iendo tasas mensuales. \277Equivale un 1 % de i)Tj
0.0517 Tc 0 Tw 459.24 0 Td
(n-)Tj
-0.0537 Tc 0.2037 Tw -459.24 -11.52 Td
(ter\351s me)Tj
0.06 Tc 0 Tw 33.6 0 Td
(n)Tj
0.0153 Tc 0.0147 Tw 4.92 0 Td
(sual a un 12 % de inter\351s anual? Raz\363nalo aplicando la f\363rmula \
del inter\351s compuesto.)Tj
/TT1 9.96 Tf
0.0234 Tc 0.2332 Tw -38.52 -11.76 Td
(Se deja para el alumno que comprueba que ambos )Tj
0.0167 Tc 0.2933 Tw 220.32 0 Td
(intereses no son equivalentes.)Tj
0.023 Tc 0.2604 Tw 126 0 Td
( La raz\363n de ello es que si el)Tj
0.0171 Tc 0.3662 Tw -346.32 -11.4 Td
(abono de intereses se realiza anualmente, hasta finalizar el primer a\361\
o el capital no se incrementa con los i)Tj
-0.0472 Tc 0 Tw 458.76 0 Td
(n-)Tj
0.0188 Tc 0.2605 Tw -458.76 -11.52 Td
(tereses; en cambio, si el abono de intereses se realiza mensualmente, al\
finalizar el)Tj
0.0151 Tc 0.2749 Tw ( primer mes ya se ve incr)Tj
0.0305 Tc 0 Tw (e-)Tj
0.0107 Tc 0.0193 Tw 0 -11.52 TD
(mentado el capital con los intereses producidos.)Tj
/TT0 9.96 Tf
0.05 Tc 0 Tw -19.56 -16.32 Td
(25.)Tj
0.0214 Tc 0.265 Tw 19.56 0 Td
(\277Cu\341ntos a\361os necesita un capital para duplicarse, seg\372n que\
est\351 colocado al 5 %, al 7 % o al 10 %? \277Puedes obt)Tj
0.0305 Tc 0 Tw 460.08 0 Td
(e-)Tj
0.0097 Tc 0.0203 Tw -460.08 -11.4 Td
(ner alguna ley para que un capital se duplique en funci\363n de la tasa)Tj
0.0167 Tc 0.0133 Tw ( de crecimiento?)Tj
/TT1 9.96 Tf
0.0176 Tc -0.0076 Tw 0 -11.76 TD
(Aproximadamente, 14, 10 y 7 a\361os, respectivamente.)Tj
0.0148 Tc 0.0252 Tw 0 -11.52 TD
(Se deja para el alumno que obtenga una ley experimental aproximada para \
ello.)Tj
/TT0 9.96 Tf
0.05 Tc 0 Tw -19.56 -17.04 Td
(26.)Tj
0.0112 Tc 0.0188 Tw 19.56 0 Td
(Se calcula que la poblaci\363n en el a\361o 2010 ser\341 el doble que en\
1975. \277Cu\341l es la tasa de crecimiento anual?)Tj
/TT2 9.96 Tf
-0.0089 Tc 0 Tw 0 -12.6 TD
(t)Tj
/TT2 6.48 Tf
0.0029 Tc 2.76 -1.56 Td
(c)Tj
/TT1 9.96 Tf
0 Tc 0.03 Tw 2.88 1.56 Td
( )Tj
/TT3 9.96 Tf
0.052 Tc 0 Tw (=)Tj
/TT1 9.96 Tf
0.03 Tc -0.06 Tw 8.16 0 Td
( 2 %)Tj
ET
/Artifact <>BDC
q
0.7071075 0.7071075 -0.7071075 0.7071075 86.548584 241.8681793 cm
0 g
/GS0 gs
0 Tc 0 Tw /Fm0 Do
Q
EMC
endstream
endobj
164 0 obj
<>>>/Resources 167 0 R/Subtype/Form>>stream
0 g 0 G 0 i 0 J []0 d 0 j 1 w 10 M 0 Tc 0 Tw 100 Tz 0 TL 0 Tr 0 Ts
BT
/Tahoma 50 Tf
0 g
0 -39.673 Td
(www.yoquieroaprobar.es) Tj
ET
endstream
endobj
165 0 obj
<>
endobj
167 0 obj
<>
endobj
168 0 obj
<>
endobj
169 0 obj
<>
endobj
170 0 obj
<>
endobj
171 0 obj
<>stream
HVyTSW/y $a$D((D l: *D{BpwCуXGD@D-Ap_QG Zǩ3Lyw} Aŏr <)nȀI{, ^ 5{rM^$ ,^9Z` Fr{ful ʲ$&{U4^2h9ON7X\HLG Ⱥ
@bO` h`(g"NJ,DX V%KLe\"_ &d!Ac=˕"DFdFw^ L L)Sm>覱 &c4@!0dϖ~ކ@83/y*=MOW!O%kJBz(eɰ}Rn7TS窇
0Rn=%aPb"2N( x$/@>t@bUʵ3F(@R; 磀8{(Zl柽V8V ]35
MrbWyS~TO|LH$:!<|WGVkÎ G\чzTrNe"9h"~D"&)0t"DB