Suppose that ​$17,965 is invested at an interest rate of 6.6 ​% per​ year, compounded continuously. ​a) Find the exponential function that describes the amount in the account after time​ t, in years. ​b) What is the balance after 1​ year? 2​ years? 5​ years? 10​ years? ​c) What is the doubling​ time? ​a) The exponential growth function is ​P(t) nothing. ​(Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the​ equation.) ​b) The balance after 1 year is ​$ nothing. ​(Simplify your answers. Round to two decimal places as​ needed.) The balance after 2 years is ​$ nothing. ​(Simplify your answers. Round to two decimal places as​ needed.) The balance after 5 years is ​$ nothing. ​(Simplify your answers. Round to two decimal places as​ needed.) The balance after 10 years is ​$ nothing. ​(Simplify your answers. Round to two decimal places as​ needed.) ​c) The doubling time is nothing years. ​(Simplify your answers. Round to one decimal place as​ needed.)