Question

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:
\[
\text{Value} = 1.0082x
\]