Suppose that \( \$ 15,684 \) is invested at an interest rate of \( 6.8 \% \) per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time \( t \), in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time? a) The exponential growth function is \( P(t)=15684 e^{0.068 t} \) (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.) b) The balance after 1 year is \( \$ 16,787.61 \). (Simplify your answers. Round to two decimal places as needed.) The balance after 2 years is \( \$ \square \). (Simplify your answers. Round to two decimal places as needed.)
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