A given field mouse population satisfies the differential equation d P _ 0.4p a40. dt where p is the number of mice and t is the time in months. (a) Find the time at which the population becomes extinct if p(O) = 1060 . Round your answer to two decimal places. ty = | 828 month(s) (c) Find the initial population p,, if the population is to become extinct in 1 year. Round your answer to the nearest integer