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Quiz 2 Math 1360 Fall 2019

Closed book, closed notes. Only a calculator is allowed. Label the problem solutions clearly,

1. Consider the system x ′ = x 2 + y 2 − 2 and y ′ = x − y. a. Sketch the nullclines, trajectory directions, equilibria, and a few representative trajectories. b. At equilibrium (1,1): Find the linearization matrix there and classify it.

2. Sparta Georgia has census data P(1970) = 5772, P(1980) = 5986. a. Assuming an exponential model find the population doubling time using P(1970) & P(1980). b. If P(1990)= 6347, find the doubling time using P(1980) & P(1990). What does your answer imply about the expo-nential model?