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Studentka2010 [4]
3 years ago
6

Una tribu de indios observa que la manada de búfalos del territorio donde se han instalado se reduce según una función de decrec

imiento exponencial dada por f(x)=kax. Hace 12 lunas contabilizaron 1944 búfalos y actualmente hay 1296 búfalos en la manada. Si se mantiene el decrecimiento exponencial, calcular dentro de cuántas lunas tendrán que abandonar la pradera, sabiendo que esa tribu cambia de territorio cuando quedan menos de de 100 búfalos.
Mathematics
1 answer:
Strike441 [17]3 years ago
5 0

Answer:

88 lunas

Step-by-step explanation:

El número inicial de búfalos, a = 1,944

El número de búfalos después de 12 semanas, y₁₂ = 1296

La forma general de una función decreciente exponencial se presenta como sigue;

y = a · bˣ

Dónde;

x = El número de lunas

b <1

a = El primer término = 1,944

Por lo tanto, tenemos;

1.296 = 1.944 × b¹²

b¹² = 1.296 / 1.944 = 2/3

b = e ^ (ln (2/3) / 12) ≈ 0,967

Cuando queden 100 búfalos, tenemos;

100 = 1.944 × (0,967)ˣ

x = ln (100 / 1.944) / ln (0,967) ≈ 87,82 ≈ 88

El número de lunas que tendrían que dejar el prado, x ≈ 88 lunas

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