# quizsoln2 - Name Math 155 Quiz 2 5 September 2006...

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Name:___________________________ Math 155 Quiz 2 5 September 2006 Instructions : This quiz is closed book and closed notes. You may use a calculator. Label your answers and show all work. 1. (5 pts) Each year, the volume (in meters cubed) of water in a pond is 3 less than 2 times its volume in the previous year. a) Write a discrete time dynamical system that represents this relationship. b) Write a discrete-time dynamical system for the mass (in kilograms) of the pond given that water has density of
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Unformatted text preview: 1000 kg m 3 . a) v t +1 = 2 v t- 3 b) m t +1 =1000 v t +1 m t +1 =1000 2 v t- 3 ( ) m t +1 = 2000 v t- 3000 m t +1 = 2000 m t 1000- 3000 m t +1 = 2 m t- 3000 2. (5 pts) Graph the following updating function and cobweb for three steps starting with the initial point x = 3 . Label the points on the cobweb diagram. Explain the long-term behavior of x . x t +1 = 3 x t- 5 (3,4) (4,7) (7,16) x t+1 x t x t +1 =3 x t- 5 Long-term behavior of x is that it grows without bound....
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