Sarah invested $8,000 in a savings account. After 10 years, her investment grew to $12,000. What is the annual interest rate, compounded continuously, that Sarah's account earned? Round your answer to the nearest two decimal places in percentage form. Use the formula A = Pe^rt, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.

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Identify Values: Identify the given values: A = $12,000 P = $8,000 t = 10 years Use the formula A = Pe^rt.Rearrange Formula: Rearrange the formula to solve for r: A = Pe^rt 12,000 = 8,000 * e^(10r) Divide both sides by 8,000: 12,000 / 8,000 = e^(10r) 1.5 = e^(10r)Take Natural Logarithm: Take the natural logarithm (ln) of both sides to solve for r: ln(1.5) = ln(e^(10r)) ln(1.5) = 10rIsolate r: Divide both sides by 10 to isolate r: r = ln(1.5) / 10Calculate r: Calculate the value of r: r ≈ ln(1.5) / 10 r ≈ 0.4055 / 10 r ≈ 0.04055Convert to Percentage: Convert r to a percentage: r ≈ 0.04055 * 100 r ≈ 4.06%

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