Consider the population model d P dt = 0.4P 1 P 230 , where P(t) is the population at time t. (a) For what values of P is the population in equilibrium? (b) For what values of P is the population increasing? (c) For what values of P is the population decreasing?

Spencer Kociba MATH 200-005 Lecture Notes Week 4 10/11/2016 Ch. 13.1 (continued) ● Graphs of Functions of 2 variables ○ 2 Space 3 Space ○ ● 3 Space surface is similar to a 2D shape that is twisted and warped ● Level Curves ○ A “topographical map” of the curve on an xy plane ○ Ex. f(x,y) =√ x + y ■ ■ Black: k=0 ■ Blue: k=1 ■ Red: k=2 ■ Peak is at k=0 ■ Shape=Cone with its point at (0,0,0) increasing in radius as z moves further to the left on the number