Question

Alguém me ajuda com essa questão de logaritimos naturais por favor

Answer 1

Obs.: Quando respondi esta questão, o editor de formulas estava com problemas. Caso os calculos estejam desformatados, considere a figura anexada.

Considerando os dados fornecidos, temos:

$\rightarrow~Q~=~100g\\\\\rightarrow~Q_o~=~500g\\\\\rightarrow~r~=~3\%~=~\frac{3}{100}\\\\\\Substituindo~os~valores~na~equacao~fornecida:\\\\\\100~=~500~.~e^{-\frac{3}{100}.t}\\\\\\\frac{100}{500}~=~e^{-\frac{3}{100}.t}\\\\\\\ e^{-\frac{3}{100}.t}~=~\frac{1}{5}\\\\\\Aplicando~o~logaritmo~natural~nos~dois~lados~da~equacao:\\\\\\ln\left(e^{-\frac{3}{100}.t}\right)~=~ln\left(\frac{1}{5}\right)\\\\\\-\frac{3}{100}.t~=~ln1-ln5\\\\\\-\frac{3}{100}.t~=~0-ln5\\\\\\t~=~-ln5~.~\left(-\frac{100}{3}\right)[\tex][tex]\\\\\\t~=~\frac{100}{3}ln5\\\\\\ou~considerando~ln5~\approx~1,61,~temos:\\\\\\t~=~\frac{100}{3}~.~1,61\\\\\\\boxed{t~=~53,67~anos}$