Question

Ryan bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it increased by 17%. During the second year the value of the stock increased by 36%. 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 apply the percentage increases successively.

1. After the first year: The stock increases by 17%. $$\text{Value after year 1}=xx+0.17\cdot xx=xx(1+0.17)=xx\cdot 1.17$$

2. After the second year: The value increases by 36% on the new stock value after the first year. $$\text{Value after year 2}=(xx\cdot 1.17)+0.36\cdot (xx\cdot 1.17)=xx\cdot 1.17(1+0.36)=xx\cdot 1.17\cdot 1.36$$

Now, we can multiply the factors: $$1.17\cdot 1.36$$

Calculating that: $$1.17\cdot 1.36=1.5912$$

Thus, the expression for the value of the stock after two years is: $$\text{Value after 2 years}=xx\cdot 1.5912$$

So, the final expression in terms of $xx$ is: $$1.5912\cdot xx$$