Question

Kaylee 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 20%. During the second year the value of the stock increased by 21%. 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, we can calculate the value step by step according to the percentage increases.

1. Initial value: Let the initial value of the stock be \( xx \) dollars.

2. After the first year: The stock increases by 20%. To find the value after this increase, we can use the expression: \[ \text{Value after 1 year} = xx + 0.20 \cdot xx = xx(1 + 0.20) = xx \cdot 1.20 \] So, the value after the first year is: \[ 1.20xx \]

3. After the second year: The stock then increases by 21%. To find the value after the second year, we apply the 21% increase to the value after the first year: \[ \text{Value after 2 years} = 1.20xx + 0.21 \cdot 1.20xx = 1.20xx(1 + 0.21) = 1.20xx \cdot 1.21 \]

4. Calculating the expression: Now we simplify \( 1.20 \cdot 1.21 \): \[ 1.20 \cdot 1.21 = 1.452 \]

5. Final expression: Thus, the value of the stock after two years is: \[ 1.452xx \]

So the final expression representing the value of the stock after two years is: \[ 1.452xx \]