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ZanzabumX [31]
3 years ago
11

13. En un pueblo, 5 personas escucharon una noticia. En una hora, cada una de ellas

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
7 0

Answer:

En 5 horas se habrá enterado todo el pueblo.

Step-by-step explanation:

Sabemos que en un pueblo 5 personas escucharon una noticia.

Una hora más tarde, cada una de ellas le contó la noticia a otras 5.

Luego, éstas contaron la noticia a otras 5 y así sucesivamente.

Nadie cuenta ni escucha la noticia más de una vez y en ese pueblo hay un poco más de 19000 habitantes.

La ecuación a desarrollar para resolver el problema es la siguiente :

Comenzamos con 5 personas que escucharon la noticia a la ''hora 0''.

Una hora más tarde, cada una de ellas le contó a 5 personas, es decir , pasada la primera hora tendremos :

5+5^{2}=30 (I)

Las 5 personas originales de la ''hora 0'' más 25 personas que se enteraron pasada la primera hora. La ecuación que planteamos es la siguiente :

5^{1}+5^{2}+5^{3}+...+5^{x}>19000 (II)

Buscamos el valor de x que satisface la ecuación (II).

Probando y realizando las sumas encontramos que :

5^{1}+5^{2}+5^{3}+5^{4}+5^{5}+5^{6}>19000

19530>19000

El valor de x que satisface (II) es x=6.

Para hallar el número de horas nos fijamos que en (I) el valor del mayor exponente del 5 es el número 2. Para ese valor 2, el tiempo que pasó es una hora.

Entonces para nuestro x=6, el número de horas que pasaron son 5 horas (1 menos que el valor de x)

Todo el pueblo se habrá enterado en 5 horas de la noticia.

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