Lucas invested $5,000 in an account to save for a trip abroad. After 7 years, his investment grew to $15,000. What is the annual interest rate, compounded continuously, that Lucas'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 values for A, P, and t. A = $15,000 P = $5,000 t = 7 yearsUse Formula: Use the formula A = Pe^(rt). Substitute A = 15,000, P = 5,000, and t = 7. 15,000 = 5,000 × e^(7r)Isolate e^(7r): Divide both sides by 5,000 to isolate e^(7r). 15,000 / 5,000 = e^(7r) 3 = e^(7r)Take Natural Logarithm: Take the natural logarithm (ln) of both sides to solve for r. ln(3) = ln(e^(7r)) ln(3) = 7rDivide by 7: Divide both sides by 7 to solve for r. r = ln(3) / 7 r ≈ 0.158 / 7 r ≈ 0.02257Convert to Percentage: Convert r to a percentage by multiplying by 100. r ≈ 0.02257 × 100 r ≈ 2.26%

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