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:
\[
1.5912 \cdot xx
\]