Question

A customer's stock value seems to be rising exponentially. The equation for the linearized regression line that models this situation is log(y) = 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 equation for the linearized regression line is:

$\log y=0.30x+0.296$

where x represents number of weeks and y be the customer's stock.

To find:

The number of weeks that will pass before the value of the stock reaches $200.

Solution:

We have,

$\log y=0.30x+0.296$

Substituting y=200, we get

$\log (200)=0.30x+0.296$

$2.301=0.30x+0.296$

$2.301-0.296=0.30x$

$2.005=0.30x$

Divide both sides by 0.30.

$\dfrac{2.005}{0.30}=x$

$6.6833333=x$

$x\approx 6.7$

Therefore, the correct option is C.