Suppose that $12,824 is invested at an interest rate of 6.5% 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) = D. (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 $|:|. (Simplify your answers. Round to two decimal places as needed.) The balance after 2 years is $|:|. (Simplify your answers. Round to two decimal places as needed.) The balance after 5 years is $|:|. (Simplify your answers. Round to two decimal places as needed.) The balance after 10 years is $|:|. (Simplify your answers. Round to two decimal places as needed.) c) The doubling time is El years. (Simplify your answers. Round to one decimal place as needed.)