After escaping from several angry camel owners (Exercise 73, Section 5.1), the spy learns that his enemy, Scelerat, is holed up in a chateau in the Alps. Disguised as an old duck plucker, the spy enters a nearby village to gather information. On the day he arrives, his identity is known only to the Redselig twins, Hans and Franz, but the next day, Hans’ girlfriend, Blabba, finds out. Soon, word about the spy’s true identity begins to spread among the 60 villagers at a rate jointly proportional to the number of people who know, N(t), and the number who do not, so that

He needs a week to gather enough information before attacking the chateau, but figures that as soon as 20 or more villagers know his identity, Scelerat will find out, too. Does our hero complete his mission or is he a dead duck plucker?

Data from Exercise 73, Section 5.1

Our spy, intent on avenging the death of Siggy Leiter (Exercise 75 in Section 4.2), is driving a sports car toward the lair of the fiend who killed his friend. To remain as inconspicuous as possible, he is traveling at the legal speed of 60 mph (88 feet per second) when suddenly, he sees a camel in the road, 199 feet in front of him. It takes him 00.7 seconds to react to the crisis. Then he hits the brakes, and the car decelerates at the constant rate of 28 ft/sec² (28 feet per second, per second). Does he stop before hitting the camel?

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dN dt = KN(60 N)