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: \[ 0.9236xx. \]