Emily received a bonus of $9,000 from her company and wants to invest it in an account to save for a dream vacation. Her investment account has a 10% interest rate compounded continuously. How long will it take for her money to grow to $24,420? Round your answer to the nearest tenth. 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 P, A, r, and t. P = 9000 A = 24420 r = 0.10Use formula: Use the formula A = Pe^(rt). 24420 = 9000 * e^(0.10 * t)Divide to isolate: Divide both sides by 9000 to isolate e^(0.10 * t). 24420 / 9000 = e^(0.10 * t) 2.7133333... = e^(0.10 * t)Take natural logarithm: Take the natural logarithm (ln) of both sides to solve for t. ln(2.7133333...) = 0.10 * tCalculate logarithm: Calculate the natural logarithm. ln(2.7133333...) ≈ 0.998 0.998 = 0.10 * tSolve for t: Solve for t by dividing both sides by 0.10. t = 0.998 / 0.10 t ≈ 9.98Round to nearest tenth: Round to the nearest tenth. t ≈ 10.0

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