Suppose that Po is invested in a savings account in which interest is compounded continuously at 6.3% per year. That is, the balance P grows at the rate given by the following equation. dP = 0.063P(t) dt (a)Find the function P(t) that satisfies the equation. Write it in terms of Po and 0.063. (b)Suppose that $500 is invested. What is the balance after 2 years? (c)When will an investment of $500 double itself? (a) Choose the correct answer below. O A. P(t) = 0.063Poet O B. P(t) = P(t) e 0.063t O C. Po= P(t) e 0.0631 O D. P(t) = Po e 0.0631 (b) The balance after 2 year is $. (Type an integer or decimal rounded to two decimal places as needed.) (c) The doubling time is | year. (Type an integer or decimal rounded to two decimal places as needed.)