Question

Audrey 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 31%. During the second year the value of the stock decreased by 34%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Answer 1

To determine the value of the stock after two years, we can break down the changes in value for each year.

1. **Initial Value**: \( xx \) dollars (the stock's value when Audrey bought it).

2. **After the first year (increase by 31%)**:
- The stock value increases by 31% of its original value. This can be expressed as:
\[
\text{Value after year 1} = xx + 0.31 \times xx = xx(1 + 0.31) = xx \times 1.31
\]

3. **After the second year (decrease by 34%)**:
- Now we apply the 34% decrease to the value at the end of the first year:
- A decrease of 34% means the stock retains 66% of its value (since 100% - 34% = 66%).
- We can express this as:
\[
\text{Value after year 2} = \text{Value after year 1} \times (1 - 0.34) = (xx \times 1.31) \times 0.66
\]

Putting this all together, the expression for the value of the stock after two years is:
\[
\text{Value after year 2} = xx \times 1.31 \times 0.66
\]

Now, multiplying the coefficients:
\[
1.31 \times 0.66 = 0.86546
\]

Thus, the final expression for the value of the stock after two years, in terms of \( xx \), is:
\[
\text{Value after two years} = xx \times 0.86546
\]