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 8%. During the second year the value of the stock decreased by 8%. 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 find the value of the stock after two years given the initial value \( xx \), we can follow these steps:
1. Calculate the value after the first year:
- The stock decreased by 8%, so it retained 92% of its value.
- The value after the first year is:
\[
xx \times (1 - 0.08) = xx \times 0.92
\]
2. Calculate the value after the second year:
- Again, the stock decreased by 8%. Thus, it will retain 92% of its value from the end of the first year.
- The value after the second year is:
\[
(xx \times 0.92) \times (1 - 0.08) = (xx \times 0.92) \times 0.92
\]
- This simplifies to:
\[
xx \times 0.92^2
\]
Now we compute \( 0.92^2 \):
\[
0.92^2 = 0.8464
\]
Thus, the expression that represents the value of the stock after two years is:
\[
xx \times 0.8464
\]
So, the final expression is:
\[
xx \times 0.8464
\]
1. Calculate the value after the first year:
- The stock decreased by 8%, so it retained 92% of its value.
- The value after the first year is:
\[
xx \times (1 - 0.08) = xx \times 0.92
\]
2. Calculate the value after the second year:
- Again, the stock decreased by 8%. Thus, it will retain 92% of its value from the end of the first year.
- The value after the second year is:
\[
(xx \times 0.92) \times (1 - 0.08) = (xx \times 0.92) \times 0.92
\]
- This simplifies to:
\[
xx \times 0.92^2
\]
Now we compute \( 0.92^2 \):
\[
0.92^2 = 0.8464
\]
Thus, the expression that represents the value of the stock after two years is:
\[
xx \times 0.8464
\]
So, the final expression is:
\[
xx \times 0.8464
\]