Suppose that Po is invested in a savings account in which interest is compounded continuously at 5.9% per year. That is, the balance P grows at the rate given by the following equation. dP at = 0.059P(t) (a)Find the function P(t) that satisfies the equation. Write it in terms of Po and 0.059. (b)Suppose that $500 is invested. What is the balance after 3 years? (c)When will an investment of $500 double itself? (a) Choose the correct answer below. O A. P(t) = 0.059Poet O B. P(t) = P(t) e 0.059t O.C. Po = P(t) e 0.059t &D. P(t) = P e 0.059t (b) The balance after 3 year is $. (Type an integer or decimal rounded to two decimal places as needed.)