Norris Romero
03/10/2024 · Elementary School

Suppose that \( \$ 16,694 \) is invested at an interest rate of \( 6.4 \% \) 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? (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for an b) The balance after 1 year is \( \$ \square \). (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.) The balance after 5 years is \( \$ \square \). (Simplify your answers. Round to two decimal places as needed.) The balance after 10 years is \( \$ \square \). (Simplify your answers. Round to two decimal places as needed.)

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The exponential function is \( A(t) = 16694 \cdot e^{0.064t} \). The balance after 1 year is \( \$ 17,734.63 \). The balance after 2 years is \( \$ 18,920.73 \). The balance after 5 years is \( \$ 22,956.73 \). The balance after 10 years is \( \$ 31,066.73 \). The doubling time is approximately \( 10.83 \) years.

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