Question

Sophia 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 34%. During the second year the value of the stock decreased by 31%. 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 break down each year's change in value step by step.

1. Initial Value: Sophia bought the stock for $xx$ dollars.

2. After the First Year: The stock increased by 34%. We calculate the new value as follows: $$\text{Value after Year 1}=xx+(34$$

3. After the Second Year: The stock then decreased by 31%. The value at the end of the second year is calculated from the value at the end of the first year: $$\text{Value after Year 2}=\text{Value after Year 1}-(31$$ Factoring out $xx(1.34)$: $$\text{Value after Year 2}=xx(1.34)(1-0.31)=xx(1.34)(0.69).$$

Thus, the final expression for the value of the stock after two years is: $$xx(1.34)(0.69).$$

4. Calculating the numerical result: $$1.34\times 0.69=0.9236.$$ So, the expression for the value of the stock after two years simplifies to: $$0.9236\cdot xx.$$

Therefore, the final value of the stock after two years is: $$0.9236xx.$$