Question
Mohal 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 24%. During the second year the value of the stock decreased by 18%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.
Answers
GPT-4o mini
To determine the value of the stock after two years, we need to apply the percentage decreases for each year to the initial value of the stock.
1. **First Year Decrease**: The stock decreases by 24%.
- The value after the first year is:
\[
x_1 = x - 0.24x = 0.76x
\]
2. **Second Year Decrease**: The stock decreases by 18% based on the new value after the first year.
- The value after the second year is:
\[
x_2 = x_1 - 0.18x_1 = 0.82x_1
\]
Substituting \( x_1 \) with \( 0.76x \):
\[
x_2 = 0.82(0.76x) = 0.6332x
\]
Thus, the expression representing the value of the stock after two years is:
\[
0.6332x
\]
1. **First Year Decrease**: The stock decreases by 24%.
- The value after the first year is:
\[
x_1 = x - 0.24x = 0.76x
\]
2. **Second Year Decrease**: The stock decreases by 18% based on the new value after the first year.
- The value after the second year is:
\[
x_2 = x_1 - 0.18x_1 = 0.82x_1
\]
Substituting \( x_1 \) with \( 0.76x \):
\[
x_2 = 0.82(0.76x) = 0.6332x
\]
Thus, the expression representing the value of the stock after two years is:
\[
0.6332x
\]