Question

9. A stock's price has been continuously declining at a rate of 5% per week. If the stock started at a price of

$62.50 per share, algebraically determine the number of weeks it will take for the price to reach $20.00 per
share. Round your answer to the nearest tenth of a week

Answer 1

After 13.6 weeks the price per share will be $20.

Explanation:

The stock's price has been continuously declining at a rate of 5% per week.

Now, if the stock's price is $62.50 per share at the start, then after w weeks the price will be
`62.5(1 - (5w)/(100) )` dollars.

Hence, we have to find the value of w if the after w week price per share is $20.

So,
`62.5(1 - (5w)/(100) ) = 20`

⇒
`1 - (w)/(20) = (20)/(62.5) = 0.32`

⇒
`(w)/(20) = 0.68`

⇒ w = 13.6 weeks

Therefore, after 13.6 weeks the price per share will be $20. (Answer)