Respuesta:
1. k = 0.02
2. La función es f(t) = 2e^(0.02t)
3. 35 min
Explicación paso a paso:
1. Calculamos el valor de "k"
2 × e^(k × 0) = 1.8 × e(5 × k)
2 × 1 = 1.8 × e^(5k)
e^(5k) = 2 / (1.8)
Aplicamos logaritmo natural
ln e^(5k) = ln (2 / (1.8))
ln (2 / (1.8)) ≈ 0.1
5k = 0.1
k = 0.1 / 5 = 0.02
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3. 2 = (2/2)e^(0.02t)
2 = e^(0.02t)
Otra vez aplicamos el logaritmo natural
ln 2 = 0.02t
t = ln 2 / 0.02
ln 2 ≈ 0.7
t = 0.7/0.02 = 35 min
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Verified answer
Respuesta:
1. k = 0.02
2. La función es f(t) = 2e^(0.02t)
3. 35 min
Explicación paso a paso:
1. Calculamos el valor de "k"
2 × e^(k × 0) = 1.8 × e(5 × k)
2 × 1 = 1.8 × e^(5k)
e^(5k) = 2 / (1.8)
Aplicamos logaritmo natural
ln e^(5k) = ln (2 / (1.8))
ln (2 / (1.8)) ≈ 0.1
5k = 0.1
k = 0.1 / 5 = 0.02
--------------------------------------------------------
2. La función es f(t) = 2e^(0.02t)
--------------------------------------------------------
3. 2 = (2/2)e^(0.02t)
2 = e^(0.02t)
Otra vez aplicamos el logaritmo natural
ln 2 = 0.02t
t = ln 2 / 0.02
ln 2 ≈ 0.7
t = 0.7/0.02 = 35 min