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Suppose that P0 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 - 0063P t) m - ' L (a)Find the function P(t) that satises the equation. Write it in terms of P0 and 0.063. (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. P0 = P\") e 0.06:\" - P(t) = 0.063Po et - P(t) = P(t) e 0-063' (b) The balance after 3 year is $|:l. (Type an integer or decimal rounded to two decimal places as) needed.) (c) The doubling time is D year. ,, . ' (Type an integer or decimal rounded to two decimal places as needed.)