Jeremy deposited x dollars in his investment account on January 1, 2001. The amount of money in the account doubled each year until Jeremy had 480 dollars in his investment account on January 1, 2005. What is the value of x ?

Explanation

To solve the problem, we need to determine the initial amount Jeremy deposited in his investment account, denoted as \( x \). The key points to note are that the amount doubles each year and that after four years (from January 1, 2001, to January 1, 2005), the total amount in the account is $480.

### Step-by-step Solution:

1. **Understand the Doubling Process**:
- On January 1, 2001, Jeremy deposited \( x \) dollars.
- After 1 year (January 1, 2002), the amount will be \( 2x \).
- After 2 years (January 1, 2003), the amount will be \( 4x \).
- After 3 years (January 1, 2004), the amount will be \( 8x \).
- After 4 years (January 1, 2005), the amount will be \( 16x \).

2. **Set up the Equation**:
- According to the problem, after 4 years, the amount in the account is $480. Therefore, we can set up the equation:
\[ 16x = 480 \]

3. **Solve for \( x \)**:
- To find \( x \), divide both sides of the equation by 16:
\[ x = \frac{480}{16} \]

4. **Calculate the Value**:
- Performing the division:
\[ x = 30 \]

5. **Conclusion**:
- The initial amount Jeremy deposited in his investment account is \( \boxed{30} \) dollars.