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.

Answer 1

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: \[ xx \times 0.8464 \]