Given:
The linearized regression line model;
[tex]\begin{gathered} \log (y)=0.30x+0.296 \\ \text{where y is the value of the stock} \\ x\text{ is the number of w}eeks \end{gathered}[/tex]Given:
y = $200
Substituting the value of y in the model to get x,
[tex]\begin{gathered} \log (y)=0.30x+0.296 \\ \log (200)=0.30x+0.296 \\ 2.301=0.30x+0.296 \\ C\text{ ollecting the like terms,} \\ 2.301-0.296=0.30x \\ 2.005=0.30x \\ \text{Dividing both sides by x,} \\ x=\frac{2.005}{0.3} \\ x=6.683 \\ x\approx6.7\text{weeks} \end{gathered}[/tex]Therefore, the best approximation of the number of weeks that will pass before the value of the stock reaches $200 is 6.7
Hence, the correct answer is option C.