Question

Shaquana 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 37%. 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 determine the value of the stock after two years based on the initial value \( xx \) and the changes in value, we can follow these steps:

1. First Year (Increase by 37%):

   • A 37% increase means the stock's value after the first year can be calculated as: \[ \text{Value after Year 1} = xx + 0.37 \cdot xx = xx(1 + 0.37) = xx \cdot 1.37 \]

2. Second Year (Decrease by 7%):

   • A 7% decrease in the value obtained after the first year means we take 7% off of the current value. The value after the second year is: \[ \text{Value after Year 2} = \text{Value after Year 1} - 0.07 \cdot \text{Value after Year 1} \] Substituting the expression from Year 1: \[ = (xx \cdot 1.37) - 0.07 \cdot (xx \cdot 1.37) \] Factor out \( xx \cdot 1.37 \): \[ = xx \cdot 1.37 (1 - 0.07) = xx \cdot 1.37 \cdot 0.93 \]

3. Final Expression: Now, we can simplify to find the final value after two years: \[ xx \cdot 1.37 \cdot 0.93 \]

Calculating \( 1.37 \cdot 0.93 \):

• \( 1.37 \cdot 0.93 = 1.27541 \)

So, the expression for the value of the stock after two years in terms of \( xx \) is: \[ xx \cdot 1.27541 \]

Thus, the final expression representing the value of the stock after two years is: \[ xx \cdot 1.27541 \]