Concept explainers
Exercises 9-14 refer to the predator-prey and the modified predator-prey systems discussed in the text (repeated here for convenience):
(i)
(ii)
14. Suppose prey move out of an area at a rate proportional to the number of predator in the area. How would you modify these systems to take this into account?
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Chapter 2 Solutions
Differential Equations
- I only need answers to questions (b) (f) (g)arrow_forwardSee imagearrow_forwardBased on the model, what is the difference in predicted amounts of milk producedbetween a cow of 5 years and a cow of 10 years? (A) (B) (C) (D) (E) A cow of 5 years is predicted to produce 5.5 fewer gallons per week.A cow of 5 years is predicted to produce 5.5 more gallons per week.A cow of 5 years is predicted to produce 1.1 fewer gallons per week.A cow of 5 years is predicted to produce 1.1 more gallons per week.A cow of 5 years and a cow of 10 years are both predicted to produce 40.8 gallons per week.arrow_forward
- You own a chocolate producing company which can advertise on both television (T) and internet(I). The effect of TV and online commercials on sales is again given by S(T,I) = 500 + 48T−6T2+ 112I−6I2+ 4TI. You have a budget of $25 that you can spend on T and I. The price of a TV commercial is $0.50 per unit and the price of an online commercial is also $0.50 per unit. 1.)Determine the optimal level of TV commercials Tand online commercials I ifyou have to spend all of your budget.You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials Tand online commercials I ifyou DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss.arrow_forwardFind the intersection points for the system below: f(x) = 2x + 14 g(x) = - 7(x + 15)2 + 11 - Round your answers to 2 decimal places a) (-4.30, 0.67), (-0.31, 0.37) O b) DNE c) (-17.11, -20.22), (-13.17, -12.35) d) (-16.00, -18.00), (-14.29, -14.57)arrow_forwardExamine the accompanying sample data for the variables y and x. Complete parts a throughd below. Uonsenh iXAN 1 4 y 1 4 a. Construct a scatter plot of these data. Describe the relationship between x and y. Choose the correct scatter plot below. OA. OB. Ос. OD. 11 11- 11- Describe the relationship between x and y. Choose the correct answer below. O A. There appears to be a negative linear relationship between x and y, because y decreasesas x increases. O B. There appears to be a negative linear relationship between x and y, because y increasesas x increases. There appears to be a positive linear relationship between x and y, because y decreases as x increases. D. There appears to be a positive linear relationship between x and y, because y increases as x increases. O E. There appears to be no relationship between x and y and (2) A 17+0 1y O O O O Oarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning