Khalil bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it decreased by 14%. During the second year the value of the stock increased by 17%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Answer 1

Let's break it down step by step to express the value of the stock after two years in terms of \( x \).

1. Initial Value: The stock was worth \( x \) dollars when Khalil bought it.

2. After Year 1: The stock decreased by 14%. Therefore, the value at the end of the first year is calculated as follows: \[ \text{Value after Year 1} = x - 0.14x = x(1 - 0.14) = x(0.86) \]

3. After Year 2: The stock then increased by 17% during the second year. To find the value at the end of the second year, we take the value at the end of Year 1 and increase it by 17%: \[ \text{Value after Year 2} = \text{Value after Year 1} + 0.17 \times \text{Value after Year 1} = \text{Value after Year 1} (1 + 0.17) \] Substituting the value from Year 1: \[ \text{Value after Year 2} = x(0.86)(1 + 0.17) = x(0.86)(1.17) \]

4. Final Expression: Now we simplify: \[ 0.86 \times 1.17 = 1.0082 \] Therefore, the expression for the value of the stock after two years is: \[ \text{Value after 2 years} = x \times 1.0082 \]

In conclusion, the value of the stock after the two years have passed can be expressed as: \[ \text{Value} = 1.0082x \]