Question

To the nearest dollar, what does the analyst believe the value of the stock will be at the end of the three weeks? (Note: Disregard the $ sign when gridding your answer.)

Answer 1

Hint: In the given question, we have been asked to find the value of stock after 3 weeks. We will find the value of the stock by the formula given i.e. \[V=360{{\left( r \right)}^{t}}\]and here, ‘t’ is equal to the time period that is 3 weeks and r is the stock value decreases i.e. V – (0.28)V = 0.72V. In this way we will put the values and get the required answer.

Complete step by step solution:
As we see that,
There is a 28% decrease in the stock value every week.
Remaining stock will be,
As the stock decreases 28 percent every week, then the remaining stock will be;
100 percent – 28 percent = 72 percent
We have 72% i.e. \[\dfrac{72}{100}\]
Converting it into decimal, we obtained
\[\dfrac{72}{100}=0.72\]
Thus,
\[r=0.72\]
Now,
The equation formed is,
\[V=360{{\left( r \right)}^{t}}\]
Substituting the values from the above, we get
\[V=360{{\left( 0.72 \right)}^{t}}\]
Here,
The time period given is three weeks,
Thus,
t = 3
Therefore,
\[V=360{{\left( 0.72 \right)}^{3}}\]
Solving the above, we get
\[V=134.47\]

Therefore,
The value of the stock after three weeks will be 134.

Note: According to analyst’s estimate the value V in dollars of the stock is decreasing by 28 percent each week for the given time period that is 3 week. The value of the stock is given by the formula \[V=360{{\left( r \right)}^{t}}\] the given equation of the value is a type of exponential decay. A stock loses 28 percent of the value each week is exactly equal to the stock’s value decreasing to 72 percent of its value of the given previous week’s value of stock.