If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at 6.1% per year, the balance P grows at the rate given by dP dt = 0.061P. a) Find the function that satisfies the equation. Write it in terms of Po and 0.061. b) Suppose that $500 is invested. What is the balance after 1 year? After 3 years? c) What is the rate of change of the balance after 1 year? After 3 years?