The island of Yavin is populated by a colony of rats. Left to their own devices,

Question

The island of Yavin is populated by a colony of rats. Left to their own devices, this colony increases in size by 16.1 percent per year.

A. Let P(t) denote the number of rats on the island after t years. Assuming a continuous model for the population growth, write down the differential equation satisfied by P(t):

P?=

B. At some point rats from the nearby island of Degobah decide to start emigrating to Yavin; they are literally coming over by the boatloads. Assume that 14000 rats emigrate to Yavin every year, and assume for simplicity that this emigration is spread out continuously over the course of the year. What differential equation models the population of Yavin now?

P?=

Explanation / Answer

(a) P' = 0.161P (b) P' = 0.161P + 14000

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