Problem 10. (10 points) You are organizing an ice cream social. The outside temperature To is 80 F and the cream is at 10 F. After 10 minutes of resting, the ice cream temperature has risen by 10 F. Assume that the temperature T(t) (a function with respect to time t) of the ice cream satisfies dT dt = k(T - To) for some constant k. . a) (5 pts) Find the constant k. . b) (5 pts) How much time does it take in total before the ice cream melts at 40 F? You can leave the answer either in simplified form or up to 2 decimal places