A dorm at a college houses 1600 students. One day, 20 of the students become ill with the flu, which spreads quickly. Assume that the total number of students who have been infected after t days is given by N(t)= 1100/1+19e^-0.65t

a) After how many days is the flu spreading the fastest? (Do not round until the final answer. Then round to two decimal places as needed.)

b) Approximately how many students per day are catching the flu on the day found in part (a)? (Round to the nearest whole number as needed.)

c) How many students have been infected on the day found in part (a)?

Please write out the steps :)