Question

Sophia bought stock in a company two years ago that was worth xx dollars. During the first year that she owned the stock, it increased by 34%. During the second year the value of the stock decreased by 31%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Answer 1

To find the value of the stock after two years, we can break down each year's change in value step by step.

1. **Initial Value**: Sophia bought the stock for \( xx \) dollars.

2. **After the First Year**: The stock increased by 34%. We calculate the new value as follows:
\[
\text{Value after Year 1} = xx + (34\% \text{ of } xx) = xx + 0.34 \times xx = xx(1 + 0.34) = xx(1.34).
\]

3. **After the Second Year**: The stock then decreased by 31%. The value at the end of the second year is calculated from the value at the end of the first year:
\[
\text{Value after Year 2} = \text{Value after Year 1} - (31\% \text{ of Value after Year 1}) = xx(1.34) - (0.31 \times xx(1.34)).
\]
Factoring out \( xx(1.34) \):
\[
\text{Value after Year 2} = xx(1.34)(1 - 0.31) = xx(1.34)(0.69).
\]

Thus, the final expression for the value of the stock after two years is:
\[
xx(1.34)(0.69).
\]

4. **Calculating the numerical result**:
\[
1.34 \times 0.69 = 0.9236.
\]
So, the expression for the value of the stock after two years simplifies to:
\[
0.9236 \cdot xx.
\]

Therefore, the final value of the stock after two years is:
\[
0.9236xx.
\]