A university endowment fund starts with $200,000 and places it in an investment account with a 5.5% interest rate compounded continuously to support future scholarships. How long will it take for the fund to grow to $350,000? 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 = 200,000 A = 350,000 r = 0.055Use formula and solve: Use the formula A = Pe^rt and solve for t. 350,000 = 200,000 * e^(0.055t)Divide and simplify: Divide both sides by 200,000. 350,000 / 200,000 = e^(0.055t) 1.75 = e^(0.055t)Take natural logarithm: Take the natural logarithm of both sides to solve for t. ln(1.75) = 0.055tCalculate ln(1.75): Calculate ln(1.75). ln(1.75) ≈ 0.5596Solve for t: Solve for t. 0.5596 = 0.055t t = 0.5596 / 0.055 t ≈ 10.1745Round to nearest tenth: Round to the nearest tenth. t ≈ 10.2 years

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