To find the expression representing the value of Deepa's stock after two years, we start with the initial value of the stock, which is \( xx \) dollars.
Step 1: Calculate the value after the first year. During the first year, the stock increased by 9%. The new value after the increase can be calculated as follows:
\[ \text{Value after Year 1} = xx + (0.09 \times xx) = xx(1 + 0.09) = xx(1.09) \]
Step 2: Calculate the value after the second year. During the second year, the stock decreased by 27%. We will apply this decrease to the value at the end of the first year:
\[ \text{Value after Year 2} = \text{Value after Year 1} - (0.27 \times \text{Value after Year 1}) \]
Substituting the value from Year 1:
\[ \text{Value after Year 2} = xx(1.09) - (0.27 \times xx(1.09)) = xx(1.09)(1 - 0.27) = xx(1.09)(0.73) \]
Final Expression: Now we can multiply out this expression:
\[ \text{Value after 2 years} = xx(1.09 \times 0.73) \]
Calculating \( 1.09 \times 0.73 \):
\[ 1.09 \times 0.73 = 0.7967 \]
Thus, the expression for the value of the stock after two years is:
\[ \text{Value after 2 years} = 0.7967xx \]
So the final expression that represents the value of the stock after two years is:
\[ 0.7967xx \]