Exercises 25—30 refer to a situation in which models similar to the predator-prey population models arise. Suppose A and B represent two substances that can combine to form a new substance C (chemists would write A + B
30. Suppose A and B are being added to the solution at constant (perhaps unequal) rates, and, in addition to the A + B
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Differential Equations
- 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.arrow_forwardConsider the discrete-time dynamical system modeling the concentration of a chemical in a lung. (Note: round all values at the end of the calculations and use 4 decimal places.)ct+1 = (1-p)ct + pβLet V = 2 L, W = 1 L, and β = 6 mmol/LIf c0 = 7 mmol/L, iterate to find the following values:c1 = ____mmol/Lc2 = ____mmol/Lc3 = ____mmol/Lc4 = ____mmol/LFind the equilibrium of this system:c* = ____mmol/Larrow_forwardIndicate which of the statement(s) below is(are) true: (a) y(t) = 3 x(t) is a linear expression %3D (b) y(t) = r(t+2) is a causal system %3D (c) y(t) = K- (t – 2) is memoryless and causal %3D O a. All of them are TRUE O b. (a) is the only TRUE statement O c. (a) and (b) are TRUE O d. (b) and (c) are TRUEarrow_forward
- An ecologist models the interaction between the tree frog (P) and insect (N) populations of a small region of a rainforest using the Lotka-Volterra predator prey model. The insects are food for the tree frogs. The model has nullclines at N=0, N=500, P=0, and P=75. Suppose the small region of the rainforest currently has 800 insects and 50 tree frogs. In the short term, the model predicts the insect population will • and the tree frog population will At another point time, a researcher finds the region has 300 insects and 70 tree frogs. In the short term, the model predicts the insect population will * and the tree frog population willarrow_forwardConsider the discrete-time dynamical system modeling the concentration of a chemical in a lung. (Note: round all values at the end of the calculations and use 4 decimal places.) ct+1 = (1 - p)ct + pβ Let V = 2 L, W = 1 L, and β = 6 mmol/L If c0 = 7 mmol/L, iterate to find the following values: c1 = ____mmol/Lc2 = ____mmol/Lc3 = ____mmol/Lc4 = ____mmol/Larrow_forwardGraph the following Discrete Dynamical Systems. Explain their long-term behavior. Try to find realistic scenarios that these DDS might explain. 7. a(n + 1) = -1.3 a(n) + 20, a(0) = 9arrow_forward
- It is linear algebra. Please see the attachmentarrow_forwardConstruct a model for the number of cats, y, after x months that make use of the following assumptions: 1. It begins with two cats – one female and one male, both unneutered. 2. Each litter is composed of 4 kittens – 3 males and 1 female. 3. It takes four months before a new generation of cats is born. 4. No cat dies (all are healthy) and no new cats are introduced.arrow_forward2.2. Consider the following matrix Y and matrix Z. Each column represents a particular meat industry. industry for beef, pork and chicken: [0.2 0.3 0.21 Y= 0.4 0.1 0.3 [0.3 0.5 0.2] [150] Z= 200 [210] For industries for beef, pork and chicken determine the total demand given by matrix Y and matrix Zarrow_forward
- Use (1) in Section 8.4 X = eAtc (1) to find the general solution of the given system. 1 X' = 0. X(t) =arrow_forward1. Suppose a population is modeled by the equation P+1 = aPe¬rP. where a and r are positive real numbers. A) Determine the equilibrium points. В) Investigate the stability of the equilibrium points.arrow_forward.The system x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7)x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7) is a special case of the Fitzhugh–Nagumo16 equations, which model the transmission of neural impulses along an axon. The parameter k is the external stimulus. a.Show that the system has one critical point regardless of the value of k.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning