Question

Nasim bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it decreased by 28%. During the second year the value of the stock increased by 35%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Answer 1

To calculate the value of the stock after two years, we will go through each year's change step-by-step.

1. **Initial Value**: The initial value of the stock is \( xx \).

2. **First Year**: The stock decreases by 28%. The value after the first year can be calculated as follows:
\[
\text{Value after first year} = xx - 0.28 \cdot xx = xx(1 - 0.28) = xx \cdot 0.72
\]

3. **Second Year**: The stock increases by 35% in the second year. We will use the value at the end of the first year as the base for the increase:
\[
\text{Value after second year} = \text{Value after first year} + 0.35 \cdot \text{Value after first year} = \text{Value after first year} \cdot (1 + 0.35)
\]
Substituting the value after the first year:
\[
\text{Value after second year} = (xx \cdot 0.72) \cdot 1.35
\]

4. **Final Expression**: Now we can simplify this expression:
\[
\text{Value after second year} = xx \cdot 0.72 \cdot 1.35
\]

Calculating \( 0.72 \cdot 1.35 \):
\[
0.72 \cdot 1.35 = 0.972
\]

So the final expression for the value of the stock after two years is:
\[
\text{Final Value} = xx \cdot 0.972
\]

Thus, the expression that represents the value of the stock after the two years have passed is:
\[
0.972xx
\]