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Blizzard
3 months ago
11

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

Mathematics
1 answer:
Leona [12.6K]3 months ago
7 0

Answer:

En un lapso de 5 horas, la noticia habrá llegado a toda la comunidad.

Step-by-step explanation:

Iniciamos con 5 individuos que conocieron la noticia.

Transcurrida una hora, cada uno de ellos comunicó la noticia a 5 más.

Las nuevas 5 personas luego se la contaron a otras 5, continuando este ciclo.

Cada persona escucha y narra la noticia solo una vez y la población del pueblo es un poco superior a 19000.

La fórmula que utilizamos para resolver este problema es la siguiente:

Empezamos con 5 personas que supieron de la noticia en el tiempo 'hora 0'.

Después de una hora, cada uno transmitió la noticia a 5 personas adicionales, lo que significa que después de la primera hora tendremos:

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

Esto incluye las 5 originales de la 'hora 0' más 25 que se enteraron en la primera hora. La fórmula que formulamos es esta:

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

Debemos hallar el valor de x que cumpla con la ecuación (II).

Al calcular y sumar, descubrimos 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 determinar el número de horas, observamos que en (I) el mayor exponente del 5 es 2. Por ese exponente, ha pasado una hora.

Así que para nuestro x=6, las horas transcurridas son 5 horas (una menos que el valor de x).

El pueblo entero conocerá la noticia a las 5 horas.

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