Under certain circumstances, a rumor spreads according to the equation:

p(t) = 1 / 1 + ae^-kt

where p(t) is the proportion of the population that knows the rumor at time t, measured in hours since the rumor first began to spread, and a and k are positive constants.

a) Assuming that the value ofacorresponds to the day of the month that you were born, andkcorresponds to the month number that you were born, what will this function look like? For instance, Fred's birthday is September 30th, so in his case a=30 and k=9, since he was born on the thirtieth day of the ninth month.

b) Based on the function that you created in Part a), find the instantaneous rate of change in the spread of the rumor exactly 3 days after it started. Round your final answer to four decimal placesof accuracy, and include units in your final answer.