Lily bought stock in a company two years ago that was worth x 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 x that represents the value of the stock after the two years have passed.

Question

Answer
Attempt 1 out of 2

Answer 1

To determine the value of the stock after two years, we can break down the increases year by year.

1. First Year:

   • The stock's initial value is \( x \) dollars.
   • It increases by 14%, which is \( 0.14x \).
   • The value of the stock after the first year is: \[ x + 0.14x = 1.14x \]

2. Second Year:

   • The stock’s value at the beginning of the second year is \( 1.14x \).
   • It then increases by 34%, which is \( 0.34 \times 1.14x \).
   • The value of the stock after the second year is: \[ 1.14x + 0.34 \times 1.14x = 1.14x(1 + 0.34) = 1.14x \times 1.34 \]

Now we can simplify that expression: \[ 1.14 \times 1.34x \]

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

Thus, the value of the stock after two years can be represented as: \[ 1.5256x \]

So the final expression for the value of the stock after two years is: \[ \boxed{1.5256x} \]