John 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 23%. During the second year the value of the stock decreased by 11%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Question

Answer

Answer 1

To determine the value of the stock after two years, we can calculate the effect of each year's percentage decrease on the initial value, denoted as \( xx \).

1. First year decrease: The stock decreases by 23%.

   • Therefore, the value of the stock after the first year is: \[ xx \times (1 - 0.23) = xx \times 0.77 \]

2. Second year decrease: The stock then decreases by 11% of its value at the end of the first year.

   • This means that the value after the second year is: \[ (xx \times 0.77) \times (1 - 0.11) = (xx \times 0.77) \times 0.89 \]

Now we can multiply these together: \[ xx \times 0.77 \times 0.89 \]

Calculating \( 0.77 \times 0.89 \): \[ 0.77 \times 0.89 = 0.6853 \]

Now substituting back into our expression: \[ \text{Value after two years} = xx \times 0.6853 \]

Thus, the expression for the value of the stock after two years is: \[ \boxed{xx \times 0.6853} \]