The stock price of one share in a certain company is worth $360 today. A stock analyst believes that the stock will lose 28 percent of its value each week for the next three weeks. The analyst uses the equation V = `360(r)^(t)` to model the value, V, of the stock after t weeks
What value should the analyst use for r ?

Explanation

To find the value of \( r \) in the equation \( V = 360(r)^t \), we need to determine how the stock price changes after losing 28% of its value each week.

### Step-by-Step Solution:

1. **Understand the Initial Value**:
The initial stock price is given as $360.

2. **Calculate the Loss**:
The stock is expected to lose 28% of its value each week. To find the remaining value after one week:
\[ \text{Loss} = 28\% \text{ of } 360 = 0.28 \times 360 = 100.8 \]
Therefore, the value after one week is:
\[ \text{Value after 1 week} = 360 - 100.8 = 259.2 \]

3. **Use the Equation**:
The equation provided is \( V = 360(r)^t \). For \( t = 1 \) (after one week), we have:
\[ V = 259.2 \]
Substituting into the equation gives:
\[ 259.2 = 360(r)^1 \]

4. **Solve for \( r \)**:
Rearranging the equation to find \( r \):
\[ r = \frac{259.2}{360} \]
Now, calculate \( r \):
\[ r = 0.72 \]

Thus, the value that the analyst should use for \( r \) is \( 0.72 \).