Question

Lily 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 14%. During the second year the value of the stock increased by 34%. 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 start with the initial value of the stock, which is \( xx \).

1. **After the first year**, the stock increases by 14%.
The value at the end of the first year is:
\[
xx + 0.14 \cdot xx = xx(1 + 0.14) = xx(1.14)
\]

2. **After the second year**, the stock increases by 34% based on its value at the end of the first year.
The value at the end of the second year is:
\[
xx(1.14) + 0.34 \cdot xx(1.14) = xx(1.14)(1 + 0.34) = xx(1.14)(1.34)
\]

Now, we can compute the final expression:
\[
xx(1.14)(1.34)
\]

Calculating \( 1.14 \times 1.34 \):
\[
1.14 \times 1.34 = 1.5256
\]

Thus, the expression for the value of the stock after two years is:
\[
xx \cdot 1.5256
\]

So the final value of the stock after two years is:
\[
\boxed{1.5256 \, xx}
\]