Hailey bought stock in a company two years ago that was worth xx dollars. During the first year that she owned the stock, it decreased by 29%. During the second year the value of the stock decreased by 24%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Question

Answer

Answer 1

To determine the value of the stock after two years, we can break this down step by step.

1. First Year: The stock decreases by 29%. This means that at the end of the first year, the value of the stock is 71% of its original value (100% - 29% = 71%).

   • The value of the stock after the first year can be represented as: \[ \text{Value after Year 1} = xx \times (1 - 0.29) = xx \times 0.71 \]

2. Second Year: The stock then decreases by another 24%. This means that at the end of the second year, the value of the stock is 76% of its value at the end of the first year (100% - 24% = 76%).

   • The value of the stock after the second year can be represented as: \[ \text{Value after Year 2} = (xx \times 0.71) \times (1 - 0.24) = (xx \times 0.71) \times 0.76 \]

Combining these expressions gives us the final value of the stock after two years: \[ \text{Final Value} = xx \times 0.71 \times 0.76 \]

Now, calculating \(0.71 \times 0.76\): \[ 0.71 \times 0.76 = 0.5376 \]

Thus, the expression for the value of the stock after two years in terms of \(xx\) is: \[ \text{Final Value} = xx \times 0.5376 \]

So, the final answer is: \[ xx \times 0.5376 \]