161:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, numérico y variacional:@0.522009:0.043661:0.926913:0.043661:0.926913:0.024916:0.522009:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 3:@0.073089:0.136836:0.148872:0.136836:0.148872:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Problema: crecimiento de bacterias:@0.073089:0.165987:0.340016:0.165987:0.340016:0.149318:0.073089:0.149318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un cultivo de bacterias tiene inicialmente 1000 bacterias. Se sabe que la población de :@0.073089:0.195138:0.710427:0.195138:0.710427:0.178704:0.073089:0.178704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
crece exponencialmente de acuerdo con la fórmula::@0.073089:0.211780:0.450918:0.211780:0.450918:0.195346:0.073089:0.195346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
N t:@0.349511:0.240931:0.370863:0.240931:0.370863:0.224525:0.349511:0.224525:0.000000:0.000000:0.000000
( ) =   :@0.360684:0.240931:0.414780:0.240928:0.414780:0.224495:0.360684:0.224497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
N e:@0.394369:0.240931:0.422492:0.240928:0.422492:0.224522:0.394369:0.224525:0.000000:0.000000:0.000000
0:@0.405559:0.241579:0.410796:0.241579:0.410796:0.231998:0.405559:0.231998:0.000000
kt:@0.422421:0.234864:0.429922:0.234864:0.429922:0.225300:0.422421:0.225300:0.000000:0.000000
donde::@0.073089:0.270078:0.124537:0.270078:0.124537:0.253644:0.073089:0.253644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.104633:0.299228:0.113137:0.299228:0.113137:0.282794:0.104633:0.282794:0.000000:0.000000
  ( ) es el número de bacterias en el tiempo   (en horas),:@0.134834:0.299228:0.535902:0.299228:0.535902:0.282794:0.134834:0.282794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
N t:@0.134834:0.299228:0.156186:0.299228:0.156186:0.282822:0.134834:0.282822:0.000000:0.000000:0.000000
t:@0.451365:0.299228:0.456740:0.299228:0.456740:0.282822:0.451365:0.282822:0.000000
• :@0.104633:0.328379:0.113137:0.328379:0.113137:0.311945:0.104633:0.311945:0.000000:0.000000
   es la población inicial,:@0.134834:0.328379:0.312574:0.328379:0.312574:0.311945:0.134834:0.311945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
N:@0.134834:0.328379:0.146081:0.328379:0.146081:0.311973:0.134834:0.311973:0.000000
0:@0.146016:0.329030:0.151252:0.329030:0.151252:0.319449:0.146016:0.319449:0.000000
• :@0.104633:0.357528:0.113137:0.357528:0.113137:0.341095:0.104633:0.341095:0.000000:0.000000
   es la constante de crecimiento, y:@0.134834:0.357528:0.382680:0.357528:0.382680:0.341095:0.134834:0.341095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.134834:0.357528:0.142399:0.357528:0.142399:0.341122:0.134834:0.341122:0.000000
• :@0.104633:0.386678:0.113137:0.386678:0.113137:0.370244:0.104633:0.370244:0.000000:0.000000
  es el tiempo en horas.:@0.134834:0.386678:0.302885:0.386678:0.302885:0.370244:0.134834:0.370244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.134834:0.386678:0.140209:0.386678:0.140209:0.370272:0.134834:0.370272:0.000000
Supongamos que después de 3 horas, la población ha aumentado a 3000 bacterias.:@0.073078:0.415829:0.679210:0.415829:0.679210:0.399395:0.073078:0.399395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.  Encontremos la constante de crecimiento  .:@0.104633:0.444979:0.452212:0.444979:0.452212:0.428545:0.104633:0.428545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.441517:0.444979:0.449083:0.444979:0.449083:0.428573:0.441517:0.428573:0.000000
b.  Encontremos la tasa de crecimiento de las bacterias en el instante   = 5 horas (es :@0.104633:0.474128:0.710309:0.474128:0.710309:0.457695:0.104633:0.457695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.607256:0.474128:0.612631:0.474128:0.612631:0.457722:0.607256:0.457722:0.000000
decir, calculemos :@0.134760:0.490770:0.263383:0.490770:0.263383:0.474336:0.134760:0.474336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dN dt:@0.263188:0.490770:0.304512:0.490770:0.304512:0.474364:0.263188:0.474364:0.000000:0.000000:0.000000:0.000000:0.000000
/  en   = 5).:@0.283565:0.490770:0.372011:0.490770:0.372011:0.474336:0.283565:0.474336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.330982:0.490770:0.336357:0.490770:0.336357:0.474364:0.330982:0.474364:0.000000
c.  Interpretemos los resultados: ¿qué le sucede a la población con el tiempo?:@0.104633:0.519920:0.674732:0.519920:0.674732:0.503486:0.104633:0.503486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 1: :@0.073096:0.549071:0.129216:0.549071:0.129216:0.532401:0.073096:0.532401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
encontremos la constante de crecimiento :@0.129109:0.549071:0.436463:0.549071:0.436463:0.532637:0.129109:0.532637:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.436142:0.549071:0.443708:0.549071:0.443708:0.532665:0.436142:0.532665:0.000000
Sabemos que al principio (cuando   = 0) hay 1000 bacterias, es decir,   = 1000. Además, :@0.073096:0.578222:0.710419:0.578221:0.710419:0.561787:0.073096:0.561788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.323950:0.578222:0.329325:0.578222:0.329325:0.561816:0.323950:0.561816:0.000000
N:@0.566999:0.578222:0.578246:0.578222:0.578246:0.561816:0.566999:0.561816:0.000000
0:@0.578179:0.581393:0.583416:0.581393:0.583416:0.571812:0.578179:0.571812:0.000000
después de 3 horas,  (3)   3000. Sustituyendo en la ecuación del crecimiento::@0.073083:0.594862:0.641202:0.594862:0.641202:0.578429:0.073083:0.578429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
N:@0.220359:0.594862:0.231606:0.594862:0.231606:0.578456:0.220359:0.578456:0.000000
5:@0.253971:0.594308:0.269304:0.594308:0.269304:0.580592:0.253971:0.580592:0.000000
3000 = 1000 :@0.333987:0.624013:0.428103:0.624013:0.428103:0.607579:0.333987:0.607579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.427938:0.624013:0.435724:0.624013:0.435724:0.607607:0.427938:0.607607:0.000000
3k:@0.435689:0.617948:0.445422:0.617948:0.445422:0.608367:0.435689:0.608367:0.000000:0.000000
Dividimos entre 1000::@0.073089:0.653162:0.230961:0.653162:0.230961:0.636728:0.073089:0.636728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3 =:@0.367495:0.682313:0.391332:0.682313:0.391332:0.665879:0.367495:0.665879:0.000000:0.000000:0.000000
 e:@0.391240:0.682313:0.402266:0.682313:0.402266:0.665907:0.391240:0.665907:0.000000:0.000000
3k:@0.402204:0.676249:0.411938:0.676249:0.411938:0.666668:0.402204:0.666668:0.000000:0.000000
Aplicamos logaritmo natural a ambos lados::@0.073089:0.711462:0.391343:0.711462:0.391343:0.695029:0.073089:0.695029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
In(3) = 3:@0.355898:0.740613:0.416082:0.740613:0.416082:0.724180:0.355898:0.724180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.415961:0.740613:0.423526:0.740613:0.423526:0.724207:0.415961:0.724207:0.000000
Despejamos  ::@0.073089:0.769764:0.177863:0.769764:0.177863:0.753330:0.073089:0.753330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.167168:0.769764:0.174734:0.769764:0.174734:0.753358:0.167168:0.753358:0.000000
k:@0.226053:0.804962:0.233619:0.804962:0.233619:0.788556:0.226053:0.788556:0.000000
 = :@0.233545:0.804962:0.252431:0.804962:0.252431:0.788528:0.233545:0.788528:0.000000:0.000000:0.000000
In(3):@0.260937:0.797235:0.293400:0.797235:0.293400:0.780801:0.260937:0.780801:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.272662:0.813627:0.281645:0.813627:0.281645:0.797193:0.272662:0.797193:0.000000
   :@0.301875:0.804959:0.325105:0.804959:0.325105:0.788525:0.301875:0.788525:0.000000:0.000000:0.000000
≈:@0.305832:0.805542:0.321166:0.805542:0.321166:0.787887:0.305832:0.787887:0.000000
1,0986:@0.339623:0.795446:0.387371:0.795446:0.387371:0.779012:0.339623:0.779012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.358987:0.811838:0.367970:0.811838:0.367970:0.795404:0.358987:0.795404:0.000000
 :@0.401858:0.804973:0.405889:0.804973:0.405889:0.788539:0.401858:0.788539:0.000000
≈ :@0.405816:0.805556:0.425659:0.805556:0.425659:0.787901:0.405816:0.787901:0.000000:0.000000
0,3662 (por hora).:@0.425659:0.804973:0.552374:0.804973:0.552374:0.788539:0.425659:0.788539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 2: :@0.073104:0.846633:0.129224:0.846633:0.129224:0.829964:0.073104:0.829964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
encontremos la tasa de crecimiento en  = 5 horas.:@0.129118:0.846633:0.494476:0.846633:0.494476:0.830199:0.129118:0.830199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 t:@0.411301:0.846633:0.419915:0.846633:0.419915:0.830227:0.411301:0.830227:0.000000:0.000000
La tasa de crecimiento se encuentra mediante la derivada de  ( ) respecto al tiempo  ::@0.073104:0.875784:0.695656:0.875784:0.695656:0.859350:0.073104:0.859350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
N t:@0.516922:0.875784:0.538274:0.875784:0.538274:0.859378:0.516922:0.859378:0.000000:0.000000:0.000000
t:@0.687152:0.875784:0.692527:0.875784:0.692527:0.859378:0.687152:0.859378:0.000000
 :@0.294838:0.908929:0.298869:0.908929:0.298869:0.892495:0.294838:0.892495:0.000000
dN:@0.301652:0.901452:0.322084:0.901452:0.322084:0.885046:0.301652:0.885046:0.000000:0.000000
dt:@0.304597:0.917844:0.319158:0.917844:0.319158:0.901438:0.304597:0.901438:0.000000:0.000000
   :@0.324956:0.908927:0.342866:0.908927:0.342866:0.892493:0.324956:0.892493:0.000000:0.000000:0.000000
=:@0.328821:0.908511:0.338927:0.908511:0.338927:0.891523:0.328821:0.891523:0.000000
d:@0.348398:0.902082:0.357657:0.902082:0.357657:0.885676:0.348398:0.885676:0.000000
dt:@0.345748:0.918474:0.360308:0.918474:0.360308:0.902068:0.345748:0.902068:0.000000:0.000000
  (   ) = :@0.363290:0.908919:0.434827:0.908920:0.434827:0.892486:0.363290:0.892485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
N e:@0.375807:0.908919:0.403831:0.908920:0.403831:0.892514:0.375807:0.892513:0.000000:0.000000:0.000000
0:@0.386990:0.909571:0.392227:0.909571:0.392227:0.899990:0.386990:0.899990:0.000000
kt:@0.403762:0.902856:0.411264:0.902856:0.411264:0.893291:0.403762:0.893291:0.000000:0.000000
N k e:@0.434643:0.908920:0.473973:0.908920:0.473973:0.892514:0.434643:0.892514:0.000000:0.000000:0.000000:0.000000:0.000000
0  :@0.445825:0.909571:0.455622:0.909571:0.455622:0.899990:0.445825:0.899990:0.000000:0.000000:0.000000
kt:@0.473914:0.902856:0.481415:0.902856:0.481415:0.893291:0.473914:0.893291:0.000000:0.000000
.:@0.481381:0.908920:0.484584:0.908920:0.484584:0.892486:0.481381:0.892486:0.000000
Interdisciplinariedad :@0.740294:0.145861:0.906668:0.145861:0.906668:0.128914:0.740294:0.128914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemáticas y:@0.740294:0.162502:0.845256:0.162502:0.845256:0.146069:0.740294:0.146069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
biología:@0.740294:0.179144:0.799337:0.179144:0.799337:0.162710:0.740294:0.162710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La relación entre el :@0.740730:0.215389:0.868833:0.215389:0.868833:0.200450:0.740730:0.200450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
crecimiento de la :@0.740730:0.230518:0.858557:0.230518:0.858557:0.215579:0.740730:0.215579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
población de bacterias :@0.740730:0.245647:0.894930:0.245647:0.894930:0.230708:0.740730:0.230708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y las derivadas permite :@0.740730:0.260776:0.895315:0.260776:0.895315:0.245836:0.740730:0.245836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entender la velocidad a la :@0.740730:0.275905:0.913427:0.275905:0.913427:0.260965:0.740730:0.260965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que la población aumenta :@0.740730:0.291034:0.918461:0.291034:0.918461:0.276094:0.740730:0.276094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en un momento específico. :@0.740730:0.306163:0.924756:0.306163:0.924756:0.291223:0.740730:0.291223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La derivada muestra que la :@0.740730:0.321292:0.921960:0.321292:0.921960:0.306352:0.740730:0.306352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tasa de crecimiento de la :@0.740730:0.336421:0.909177:0.336421:0.909177:0.321481:0.740730:0.321481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
población es proporcional :@0.740730:0.351550:0.917579:0.351550:0.917579:0.336610:0.740730:0.336610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a la cantidad actual de :@0.740730:0.366679:0.892483:0.366679:0.892483:0.351739:0.740730:0.351739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bacterias. Esto significa :@0.740730:0.381808:0.894993:0.381808:0.894993:0.366868:0.740730:0.366868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que a medida que hay :@0.740730:0.396937:0.892466:0.396937:0.892466:0.381997:0.740730:0.381997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
más bacterias, la población :@0.740730:0.412066:0.922450:0.412066:0.922450:0.397126:0.740730:0.397126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
crece cada vez más rápido, :@0.740730:0.427195:0.920768:0.427195:0.920768:0.412255:0.740730:0.412255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lo cual es característico del :@0.740730:0.442324:0.920482:0.442324:0.920482:0.427384:0.740730:0.427384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
crecimiento exponencial.:@0.740730:0.457453:0.906710:0.457453:0.906710:0.442513:0.740730:0.442513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esta derivada es útil para :@0.740730:0.585632:0.906638:0.585632:0.906638:0.570693:0.740730:0.570693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entender y calcular cómo :@0.740730:0.600761:0.912612:0.600761:0.912612:0.585822:0.740730:0.585822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
varía la población en :@0.740730:0.615890:0.880937:0.615890:0.880937:0.600951:0.740730:0.600951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cada instante, y también :@0.740730:0.631019:0.905631:0.631019:0.905631:0.616079:0.740730:0.616079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
permite analizar aspectos :@0.740730:0.646148:0.912420:0.646148:0.912420:0.631208:0.740730:0.631208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como el tiempo necesario :@0.740730:0.661277:0.917065:0.661277:0.917065:0.646337:0.740730:0.646337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para duplicar la población :@0.740730:0.676406:0.915850:0.676406:0.915850:0.661466:0.740730:0.661466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(utilizando la constante  ).:@0.740730:0.691535:0.911968:0.691535:0.911968:0.676595:0.740730:0.676595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.897878:0.691535:0.904756:0.691535:0.904756:0.676620:0.897878:0.676620:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000