Question

Makayla bought stock in a company two years ago that was worth xx dollars. During the first year that she owned the stock, it increased by 12%. 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

To find the value of the stock after two years, we can write the changes in terms of \( xx \).

1. After the first year: The stock increases by 12%. The value of the stock after the first year can be calculated as follows:

   \[ \text{Value after first year} = xx + 0.12 \cdot xx = xx \cdot (1 + 0.12) = xx \cdot 1.12 \]

2. After the second year: The stock decreases by 7%. To find the value after the second year, we apply the 7% decrease to the value at the end of the first year:

   \[ \text{Value after second year} = (xx \cdot 1.12) - 0.07 \cdot (xx \cdot 1.12) = (xx \cdot 1.12) \cdot (1 - 0.07) = (xx \cdot 1.12) \cdot 0.93 \]

   Simplifying this expression gives:

   \[ \text{Value after second year} = xx \cdot 1.12 \cdot 0.93 \]

3. Calculating the final expression:

   Now we can calculate \( 1.12 \cdot 0.93 \):

   \[ 1.12 \cdot 0.93 = 1.0436 \]

Thus, the expression representing the value of the stock after two years is:

\[ \text{Value after two years} = xx \cdot 1.0436 \]

This means that after two years, the value of the stock is approximately 1.0436 times the original value \( xx \).