Question

Sophia bought stock in a company two years ago that was worth x 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. simplify or something

Answer 1

To find the value of the stock after two years, we can break down the changes in value year by year.

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

2. **After the First Year**: The stock increased by 34%. To find the value after the first year, we calculate:
\[
\text{Value after year 1} = x + 0.34x = 1.34x
\]

3. **After the Second Year**: The stock then decreased by 31%. To find the value after the second year, we calculate:
\[
\text{Value after year 2} = 1.34x - 0.31(1.34x) = 1.34x(1 - 0.31) = 1.34x \cdot 0.69
\]

4. **Calculation**: Now we simplify:
\[
1.34 \times 0.69 = 0.9246
\]

Thus, the value of the stock after two years can be expressed as:
\[
\text{Value after two years} = 0.9246x
\]

So the expression in terms of \( x \) is:
\[
0.9246x
\]