Matematicas La Peste Negra

y (t) ꞊ 2000 1+3𝑒 βˆ’0.8𝑑 2. t꞊0 y(t) ꞊ y(t) ꞊ 2000 1+3𝑒 βˆ’0.8(0) 2000 4 y(t) ꞊ 500 personas 3. t꞊3 y(t) ꞊ y(t) ꞊ 20

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y (t) ꞊

2000 1+3𝑒 βˆ’0.8𝑑

2. t꞊0 y(t) ꞊ y(t) ꞊

2000 1+3𝑒 βˆ’0.8(0) 2000 4

y(t) ꞊ 500 personas

3. t꞊3 y(t) ꞊ y(t) ꞊

2000 1+3𝑒 βˆ’0.8(3) 2000 1.272153

y(t) ꞊ 1572.13 personas 4. t

0

1

2

3

4

5

6

7

8

9

10

11

20

y 500 851.79 1245.57 1572.13 1782.07 1895.82 1951.81 1978.05 1990.08 1995 1997 1999 1999.999

t

25

29

30

100

1000

y

1999.999988

1999.999999

2000

2000

2000

5. t꞊? 1.978꞊ 1+

2000 1+3𝑒 βˆ’0.8(𝑑)

βˆ’0.8(𝑑) 2000 3𝑒 ꞊ 1978

βˆ’0.8(𝑑) 2000 3𝑒 ꞊ -1 1978

log 𝑒

βˆ’0.8(𝑑)

꞊ log

0.0111 3

βˆ’0.8𝑑 log 𝑒 ꞊ log 3.7 Γ— 10βˆ’3

t꞊[

log 3.7Γ—10βˆ’3 log 𝑒

βˆ’0.8

βˆ’0.8988877654

]

t ꞊ 6.9999 β‰ˆ 7 semanas