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: \[ 0.9246x \]