1. (8 points) If an amount P0, in dollars, is invested with interest compounded continuously P at 5.9% per year, the balance P grows at the rate given by (:7 = 0.059P. P (i) Find the function that satises the equation ddt = 0.059P. Write it in terms of P0 and 0.059. (ii) Suppose that $1000 is invested. What is the balance after 2 years? (iii) If $1000 is invested, how fast (i.e., rate of change) is the balance growing after 2 years? (iv) When will an investment of $1000 double itself