Question

Shaquana 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 37%. During the second year the value of the stock decreased by 7%. Write an expression in terms of x 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 follow the changes in value step-by-step.

1. **Initial value of the stock:**
The initial value of the stock is \( x \) dollars.

2. **After the first year:**
The stock increases by 37%. The new value after the first year can be calculated as follows:
\[
\text{Value after first year} = x + 0.37x = x(1 + 0.37) = x(1.37).
\]

3. **After the second year:**
The stock then decreases by 7%. A 7% decrease on the value after the first year can be calculated as:
\[
\text{Value after second year} = x(1.37) - 0.07(x(1.37)) = x(1.37)(1 - 0.07) = x(1.37)(0.93).
\]

Putting it all together, the expression for the value of the stock after two years is:
\[
x(1.37)(0.93).
\]

Now we can simplify that:
\[
1.37 \times 0.93 = 1.2761.
\]
Thus, the expression simplifies to:
\[
1.2761x.
\]

Therefore, the value of the stock after two years is:
\[
\boxed{1.2761x}.
\]