Suppose that Po is invested in a savings account in which interest is compounded continuously at 7.1% per year. That is, the balance P grows at the rate given by the following equation. Natural dP dt = 0.071P(t) (a)Find the function P(t) that satisfies the equation. Write it in terms of Po and 0.071. (b)Suppose that $500 is invested. What is the balance after 1 years? ithmic fun (c)When will an investment of $500 double itself? (a) Choose the correct answer below. O A. P(1) = Poe 0.0711 functions a O B. P(1) = 0.071Poel 15 O C. P(1) = P(t) e 0.0711 h of natural OD. Po = P(t) e 0.0711 wth Models (b) The balance after 1 year is $ (Type an integer or decimal rounded to two decimal places as needed ) ited growth . (c) The doubling time is year. (Type an integer or decimal rounded to two decimal places as needed.)