01 -(UNI-RIO-2002) Numa população de bactérias , há p(t)=10^9.4^3t bactérias no instante t medido em horas (ou fração da hora). Sabendo-se que inicialmente existem 10^9 bactérias, quantos minutos são necessários para que se tenha dobro da população inicial ?
Exemplo: 
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Boa tarde!
Solução!
![P(t)=10^{9}.4^{3t} \\\\\\
Dobro=2\\\\\
T_{0}= 10^{9}](https://tex.z-dn.net/?f=P%28t%29%3D10%5E%7B9%7D.4%5E%7B3t%7D+%5C%5C%5C%5C%5C%5C%0ADobro%3D2%5C%5C%5C%5C%5C%0AT_%7B0%7D%3D+10%5E%7B9%7D+ "P(t)=10^{9}.4^{3t} \\\\\\
Dobro=2\\\\\
T_{0}= 10^{9}")
![2(10^{9})=10^{9}.4^{3t} \\\\\\
2\dfrac{10^{9}}{10^{9}}=4^{3t}\\\\\\
2= 4^{3t}\\\\
2^{1}=2^{2}^{(3t)}\\\\\\
2^{1}=2^{6t}\\\\\\
6t=1\\\\\\
t= \dfrac{1}{6}\\\\\\
Logo!\\\\\\
t= \dfrac{1}{6}\times 60 \\\\\\\\\\
t= \dfrac{60}{6} \\\\\\\\\
t=10](https://tex.z-dn.net/?f=2%2810%5E%7B9%7D%29%3D10%5E%7B9%7D.4%5E%7B3t%7D+%5C%5C%5C%5C%5C%5C%0A+2%5Cdfrac%7B10%5E%7B9%7D%7D%7B10%5E%7B9%7D%7D%3D4%5E%7B3t%7D%5C%5C%5C%5C%5C%5C%0A2%3D+4%5E%7B3t%7D%5C%5C%5C%5C%0A2%5E%7B1%7D%3D2%5E%7B2%7D%5E%7B%283t%29%7D%5C%5C%5C%5C%5C%5C%0A+2%5E%7B1%7D%3D2%5E%7B6t%7D%5C%5C%5C%5C%5C%5C%0A6t%3D1%5C%5C%5C%5C%5C%5C%0At%3D+%5Cdfrac%7B1%7D%7B6%7D%5C%5C%5C%5C%5C%5C%0ALogo%21%5C%5C%5C%5C%5C%5C%0At%3D+%5Cdfrac%7B1%7D%7B6%7D%5Ctimes+60+%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0At%3D+%5Cdfrac%7B60%7D%7B6%7D+%5C%5C%5C%5C%5C%5C%5C%5C%5C%0At%3D10++ "2(10^{9})=10^{9}.4^{3t} \\\\\\
2\dfrac{10^{9}}{10^{9}}=4^{3t}\\\\\\
2= 4^{3t}\\\\
2^{1}=2^{2}^{(3t)}\\\\\\
2^{1}=2^{6t}\\\\\\
6t=1\\\\\\
t= \dfrac{1}{6}\\\\\\
Logo!\\\\\\
t= \dfrac{1}{6}\times 60 \\\\\\\\\\
t= \dfrac{60}{6} \\\\\\\\\
t=10")
Boa tarde!
Bons estudos!
Solução!
Boa tarde!
Bons estudos!
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