3. Consider the linear system = x-(7)x (a) Find all equilibrium points. (b) Let |x(t)| denote the magnitude of the solution X(t). Find an ODE that's satisfied by |x(t)|². (c) Find the solution of the initial value problem with X(0) : = and sketch it in the plane. Determine the type of the equilibrium points.

Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.

D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. D(x) = ex+2.5, S(x) = ex- 7.5 a) Find the equilibrium point. b) Find the consumer surplus at the equilibrium point. c) Find the producer surplus at the equilibrium point. a) What are the coordinates of the equilibrium point? --- (Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Do not include the $ symbol in your answer) b) What is the consumer surplus at the equilibrium point? $ (Round to the nearest cent as needed.) c) What is the producer surplus at the equilibrium point? (Round to the nearest cent as needed.)

D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. D(x) = e X+2 S(x) = e x-6 a) Find the equilibrium point. b) Find the consumer surplus at the equilibrium point. c) Find the producer surplus at the equilibrium point. a) What are the coordinates of the equilibrium point? (Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Do not include the $ symbol in your answer)