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
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
DIFFERENTIAL EQUATIONS-ACCESS
- 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 dynamical system Yk=1 = log (yk) + Yk- Which of the following statements is true about the dynamical system? O The dynamical system has infinite fixed points. The dynamical system has only one fixed points. The dynamical system has.no fixed points.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_forward
- Indicate 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_forwardAn 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 example of injection moulding of a rubber component as shown in Figure Q3(b). The process engineer would like to optimise the strength of the component by optimising the following factors: temperature = 190°C and 210°C, pressure = 50 MPa and 100 MPa, and speed of injection = 10 mm/s and 50 mm/s. What type of mathematical model that the engineer can develop if the relationship is linear and no interactions are significant? Write down the general equation that relates the strength of the component with the process factors.arrow_forward
- Consider 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_forwardHermann Ebbinghaus (1850–1909) pioneered the study of memory. A 2011 article in the Journal of Mathematical Psychology presents the mathematical model R(t) = a + b(1 + ct)−? for the Ebbinghaus forgetting curve, where R(t) is the fraction of memory retained t days after learning a task; a, b, and c are experimentally determined constants between 0 and 1; ? is a positive constant; and R(0) = 1. The constants depend on the type of task being learned. (a) What is the rate of change of retention t days after a task is learned?arrow_forwardA system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the remaining pump is now more likely to fail than was originally the case. That is, r = P(#2 fails | #1 fails) > P(#2 fails) = q. a) If at least one pump fails by the end of the pump design life in 7% of all systems and both pumps fail during that period in only 1%, what is the probability that pump #1 will fail during the pump design life? b) If pump #1 fails what is the probability that pump #2 will fail during the pump design life?arrow_forward
- Section 3.1 1. Rewrite the specified linear system in matrix form. 2. Rewrite the specified linear system in component form. dx = 2x + y dt dx dt dy dy = x +y dt dtarrow_forwardQ.4 Baiji north Refinery use kirkuk crude oil(API=36) with total flowrate 150000 BBL/ Day(the price of one BBI of crude oil=87000 Iraqi Dinar).It has the following products: Gasoline 20%(one litre price=450 Iraqi Dinar),Kerosine 15% (one litre price=150 Iraqi Dinar),Gas oil 20%(one litre price-400 Iraqi Dinar).and 45% remaining is Black oil(one litre price-50 Iraqi Dinar). Is this Refinery Win or Lose?arrow_forwardQuestion No. 2) Explain the importance of fixed point in discrete dynamical Systems with the help of two practical examples.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,