Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{M = C \times (1 + i)^t}\rightarrow\begin{cases}\mathsf{M = montante}\\\mathsf{C = capital}\\\mathsf{i = taxa}\\\mathsf{t = tempo}\end[/tex]
[tex]\mathsf{200 = 100 \times (1 + 0,02)^t}[/tex]
[tex]\mathsf{200 = 100 \times (1,02)^t}[/tex]
[tex]\mathsf{(1,02)^t = \dfrac{200}{100}}[/tex]
[tex]\mathsf{(1,02)^t = 2}[/tex]
[tex]\mathsf{log\:(1,02)^t = log\:2}[/tex]
[tex]\mathsf{t\:log\:(1,02) = log\:2}[/tex]
[tex]\mathsf{t = \dfrac{log\:2}{log\:1,02}}[/tex]
[tex]\mathsf{t = \dfrac{0,3010}{0,0086}}[/tex]
[tex]\boxed{\boxed{\mathsf{t = 35}}}\leftarrow\textsf{meses}[/tex]
