Question

Jordan bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it decreased by 7%. During the second year the value of the stock decreased by 7%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Answer 1

Let's denote the initial value of the stock as \( x \).

During the first year, the stock decreases by 7%. The value of the stock after the first year can be calculated as follows:

\[ \text{Value after first year} = x - 0.07x = x(1 - 0.07) = x(0.93) \]

Now, during the second year, the stock again decreases by 7%. The value of the stock after the second year can be calculated using the value at the end of the first year:

\[ \text{Value after second year} = (0.93x) - 0.07(0.93x) = 0.93x(1 - 0.07) = 0.93x(0.93) \]

Now, let's simplify that expression:

\[ \text{Value after second year} = 0.93 \times 0.93 \times x = 0.8649x \]

Thus, the expression in terms of \( x \) that represents the value of the stock after two years is:

\[ 0.8649x \]