Math 116 / Final (December 12, 2014)page 87. [14 points] Chickens continue to appear around you, and Franklin’s army is hesitant to advance.a. [6 points] LetF(t) give the total number of chickens that have arrived aftertseconds.You observe thatF(t) obeys the following differential equationdFdt=e−Ft2.If there are initially 20 chickens, find a formula (in terms oft) forF(t).
b. [4 points] A large, familiar-looking chicken steps forward from the flock and clucks, “KooKoo Katcha!”.This large chicken waddles towards Franklin following the parametricequationsx(t) =sin(πt) + 1πy(t) = ln(t+ 1)wheretis the time, in seconds, after the chicken steps forward from the flock and bothxandyare measured in feet. Find the chicken’s speed 10 seconds after it steps forward.Include units.
University of Michigan Department of Mathematics