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{cases}[/tex]
[tex]\mathsf{20.250 = 1.350 \times (1 + 0,012)^t}[/tex]
[tex]\mathsf{20.250 = 1.350 \times (1,012)^t}[/tex]
[tex]\mathsf{(1,012)^t = \dfrac{20.250}{1.350}}[/tex]
[tex]\mathsf{(1,012)^t = 15}[/tex]
[tex]\mathsf{log\:(1,012)^t = log\:15}[/tex]
[tex]\mathsf{t\:log\:(1,012) = log\left(3\:.\:\dfrac{10}{2}\right)}[/tex]
[tex]\mathsf{t\:log\:(1,012) = log\:3 + log\:10 - log\:2}[/tex]
[tex]\mathsf{t = \dfrac{0,477 + 1 - 0,301}{0,0052}}[/tex]
[tex]\boxed{\boxed{\mathsf{t \approx 226,15}}}\leftarrow\textsf{meses}[/tex]
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Verified answer
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{cases}[/tex]
[tex]\mathsf{20.250 = 1.350 \times (1 + 0,012)^t}[/tex]
[tex]\mathsf{20.250 = 1.350 \times (1,012)^t}[/tex]
[tex]\mathsf{(1,012)^t = \dfrac{20.250}{1.350}}[/tex]
[tex]\mathsf{(1,012)^t = 15}[/tex]
[tex]\mathsf{log\:(1,012)^t = log\:15}[/tex]
[tex]\mathsf{t\:log\:(1,012) = log\left(3\:.\:\dfrac{10}{2}\right)}[/tex]
[tex]\mathsf{t\:log\:(1,012) = log\:3 + log\:10 - log\:2}[/tex]
[tex]\mathsf{t = \dfrac{0,477 + 1 - 0,301}{0,0052}}[/tex]
[tex]\boxed{\boxed{\mathsf{t \approx 226,15}}}\leftarrow\textsf{meses}[/tex]