To determine how much Ling deposited initially, we can use the formula for continuous compounding:

$A = P \cdot e^{rt}$

Where:

• $A$ is the current amount in the account (final amount),
• $P$ is the initial deposit (the value we need to find),
• $r$ is the interest rate (as a decimal),
• $t$ is the time in years,
• $e$ is Euler's number (approximately 2.71828).

Given:

• $A = 2000$,
• $r = 9\% = 0.09$,
• $t = 7$ years.

Now, we rearrange the formula to solve for $P$:

$P = \frac{A}{e^{rt}}$

Substitute the known values:

$P = \frac{2000}{e^{0.09 \cdot 7}}$

Let's compute that.Ling initially deposited approximately $1,065.18 in her savings account.

Would you like any additional details or explanations?

Here are 5 related questions to deepen your understanding:

1. What is the formula for compound interest (not continuous)?
2. How would the initial deposit change if the interest rate were 8% instead of 9%?
3. What if the interest were compounded yearly instead of continuously?
4. How would the balance change if she had deposited $3,000 instead of $2,000?
5. What is Euler's number, and why is it used in continuous compounding?

Tip: Continuous compounding means the interest is being added to the principal constantly, which results in the fastest growth compared to other compounding intervals.