Question

A customer's stock value seems to be rising exponentially. The equation for the linearized regression line that models this situation is log() = 0.30x +0.296, where x represents number of weeks. Which of the following is the best approximation of the number of weeks that will pass before the value of the stock reaches $200? A. 9.3 B. 12.1 C. 6.7 D. 4.8

Answer 1

Given:

The linearized regression line model;

`\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}`

Given:

y = $200

Substituting the value of y in the model to get x,

`\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=(2.005)/(0.3) \\ x=6.683 \\ x\approx6.7\text{weeks} \end{gathered}`

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.