Answer:
Audrey will have $10,498.10 when Zoe's money has doubled in value.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Algebra I
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Algebra II
Natural Logs and Exponentials
Compounded Continuously Interest Rate Formula:

- P is the principle amount
- r is the interest rate
- t is time
Compounded Annually Interest Rate Formula:

- P is the principle amount
- r is the interest rate
- t is time
Explanation:
Step 1: Define
Identify.
Zoe:
P = $5,500
r = 0.085
A = 2P
Aubrey:
P = $5,500
r = 0.0825
Step 2: Find Time
Find time elapsed by using Zoe.
- Substitute in variables [Compounded Continuously Interest Rate]:

- Substitute in P:

- Simplify:

- Isolate t term:

- Isolate t:

So the time it takes for Zoe to get double her money is approximately 8.15467 years.
Step 3: Find Audrey's Money
- Substitute in variables [Compounded Annually Interest Rate]:

- Evaluate:

∴ after the elapsed time of approximately 8.15467 years, Zoe would have made double her money valued at $11,000 and Audrey would have made $10,498.10.
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Topic: Algebra II
Unit: Logarithmic Functions