En cierto cultivo, inicialmente había 1000 amebas que se reproducen por biparticion cada día ¿Cuántas amebas habrá al cabo de 30 días después que se inició el cultivo ?

Answer: 1,073,741,824,000 amebas

Step-by-step explanation:

Bipartición significa que la población de amebas se duplica cada día.

Entonces si inicialmente hay 1000, después de un día van a haber:

2*1000.

Después del segundo día se vuelven a duplicar, entonces van a haber:

2*(2*1000) = (2^2)*1000

Después del tercer día, lo mismo:

2*(2^2)*1000 = (2^3)*1000.

A esta altura ya se puede ver el patrón, podemos concluir que después de N días, la población de amebas va a ser:

P(N) = (2^N)*1000.

Entonces respondiendo a la pregunta:

¿Cuántas amebas habrá al cabo de 30 días después que se inició el cultivo?

Tenemos que tomar N = 30

P(30) = (2^30)*1000 = 1,073,741,824,000 amebas

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