(i) Give a biological meaning of the terms rN and -rN VN/K in the right hand side ofthe equation (1) and of the parameters r and K.(ii) Sketch the graph of the function in the right hand side of equation (1) for N > 0. Uscyour sketch to show that the system has a single non-zero equilibrium, determine itsstability and clearly indicate the stability of the steady state on your graph usingarrows. The dynamics of a fish population is described by the Richard's growth lawdNNrN(1)dtKwhere N = N(t) is the population size depending on the continuous time variable t, and rand K are positive constants.

Given: The dynamics of a fish population, described by the Richard's growth law, dNdt=rN1-NK, where…

Answered: (i) Give a biological meaning of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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. If the equilibrium price is $12 and the equilibrium quantity is 144 units, find the Consumer Surplus at the equilibrium point and then answer the question about Producer Surplus. 144 D(x)= S(x) = Vx %3D You must write a complete solution for part (a) and submit with your written work. Note: Consumer and Producer Surplus formulas are: Consumer Surplus: D(x)dx- PQ, Producer Surplus: PQ- | Sx)dx. [4 points] (a) The Consumer Surplus is S (Round to the nearest cent as needed.) (b) Which expression will give the correct value of the Producer Surplus? [2 points] O A. T 1 1A-(12|144) 0. -144 -(12)(144) |O B. 21 (12)(144)- [144 -0 OC. 3 2. 2, 21 144 3. (12)(144) D. 31 (12)(144)- 2. 144 E. (12)(144)- [12 -0 (Select the correct answer.) Click to select your answer(s).
(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.
6. The monthly supply and demand functions for extra fancy green tea are: Supply function: q= 5p- 74 Demand function: q -4p+70 %3D where p price per pound (in dollars), and hundreds of pounds sold at price p. (a Find the equilibrium price. (b How many pounds of green tea are sold at this price?
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Consider the demand (D) and supply (S) functions D = 14 - P and S = P² + 3P +2. (P is the unit price by dollars.) 1. Find the domain of the function D = D(P) in this context. 2. Find the equilibrium price Pr. What happens if P > P* (explain in this context)? ( 3. Sketch both the demand and supply curves in one coordinate system. Identify the equilibrium point...
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)
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. Find (a) the equilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point. 1 5 D(x)=x+11, S(x)=x+4 3 (a) Find the equilibrium point (Type an ordered pair, using integers or decimals.) (b) Find the consumer surplus at the equilibrium point. $(Type an integer or a decimal.) (c) Find the producer surplus at the equilibrium point. $ (Type an integer or a decimal.)

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