Plants depend on microbial partners (bacteria and fungi) within soil to provide them with nitrogen (in return, the plant provides its microbial partners with sugars). We will build a two-compartment model for the available nitrogen in the system. Measure time, t, in days. Let x, represent the amount of nitrogen held by soil fungi, and let X, represent the amount of nitrogen held by the plant. Assume that in one day the fungi gain (from the atmosphere) 1 g of nitrogen. Assume also that in one day they pass 50% of their free nitrogen to the plant, and they use up 20% of this nitrogen for growth. In the plant, 90% of the nitrogen is used up (e.g., for growth) each day, but no nitrogen is returned to the fungal partner. Complete parts (a) through (c).

Plants depend on microbial partners (bacteria and fungi) within soil to provide them with nitrogen (in return, the plant provides its microbial partners with sugars). We will build a two-compartment model for the available nitrogen in the system. Measure time, t, in days. Let x, represent the amount of nitrogen held by soil fungi, and let X, represent the amount of nitrogen held by the plant. Assume that in one day the fungi gain (from the atmosphere) 1 g of nitrogen. Assume also that in one day they pass 50% of their free nitrogen to the plant, and they use up 20% of this nitrogen for growth. In the plant, 90% of the nitrogen is used up (e.g., for growth) each day, but no nitrogen is returned to the fungal partner. Complete parts (a) through (c).

Name: Plants depend on microbial partners (bacteria and fungi) within soil
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: Plants depend on microbial partners (bacteria and fungi) within soil to provide them with nitrogen (in return, the plant provides its microbial partners with sugars). Wewill build a two-compartment model for the available nitrogen in the system. Mea

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: The price-demand equations x = f(p, q) and y = g(p, q) represent the num- ber of units demanded of…

A: The weekly price demand equation for A and B. So, the given equation is, (a) It is known that,…

Q: Animals and people that take in more energy than they expend will get fatter. Here are data on 12…

A: Given:The data of the body mass and energy of Lean and obese monkeys is provided…

Q: The table below shows the projected values (in millions of dollars) of hardback college textbooks…

A: Consider the provided question, The table below shows the projected values (in millions of dollars)…

Q: 3. Two experimental lines of botflies reproduce at different rates. These equations represent the…

A: Here the function used to represent the number of bot flies are exponential functions. An…

Q: Model the situation with a dynamical system. Use your model to answer the question. 12) You take a…

Q: Find the production schedule for the technology matrix and demand vector given below: [0.3 0.4 A =…

Q: Find the production schedule for the technology matrix and demand vector given below: 0.2 0.6 4 A =…

Q: Suppose we are able to model the total utility function for the consumption of two goods, good x and…

A: Given Utility Function : U(x, z) = 3x2 + z2 - 2xz Px = Py = $1 Total Income = $1000

Q: A $25,000 machine depreciates linearly to 0 over a 10 year period. What is the valye of the machine…

Q: For the two graphs below, which of the following are equilibrium points? Revenue Supply Cost B.…

A: The equilibrium price is the market price the quantity of goods supplied is equal to the quantity of…

Q: A new town was incorporated in 1960. The size of the town's population was recorded every 5 years…

A: Introduction: Simple linear regression model: A simple linear regression model is given as y^ = b0…

Q: Suppose an economy has only two sectors: Goods and Services. Each year, Goods sells 80% of its…

A: It is required to find the equilibrium prices for the annual outputs of the Goods and Services…

Q: The demand for watches is given by p = 7000 − 2q dollars, and the supply of watches is given by p =…

Q: Two connected tanks, each with a capacity of 50 liters, contain brine (saltwater). Initially, the…

A: In tank 1, the initial amount of Brine is 18 ltrs with a concentration of 3gms/ltr. In tank 2, the…

Q: Elizabeth Swann and her husband consume wine (W) and books (B). Elizabeth's utility function is…

A: Elizabeth Swann and her husband consume wine (W) and books (B).

Q: represent the number of bacteria (measured in millions) at time t (measured in hours). This system…

Topic Video

Question

Plants depend on microbial partners (bacteria and fungi) within soil to provide them with nitrogen (in return, the plant provides its microbial partners with sugars). We
will build a two-compartment model for the available nitrogen in the system. Measure time, t, in days. Let x, represent the amount of nitrogen held by soil fungi, and let
X, represent the amount of nitrogen held by the plant. Assume that in one day the fungi gain (from the atmosphere) 1 g of nitrogen. Assume also that in one day they
pass 50% of their free nitrogen to the plant, and they use up 20% of this nitrogen for growth. In the plant, 90% of the nitrogen is used up (e.g., for growth) each day, but
no nitrogen is returned to the fungal partner. Complete parts (a) through (c).
(a) Draw a compartment diagram showing the flows of nitrogen between fungi and plant. Choose the correct diagram below.
A.
O B.
OD.
1.0
0.5x
1.0
1.0
1.0
0.9x
0.5x
X1
X2
X1
X2
X1
X2
X1
0.9x-
1.0
0.3x
0.5x,
0.2x
0.9x,
0.2x,
0.9x,
0.2
0.5
(b) Write down a system of differential equations for x, (t) and x, (t).
dx1
dt
dx2
dt
모모

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 10 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Optimization$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

A company makes two grades of paint, grade I, guaranteed for 5 years, and grade II, guaranteed for 10 years. A gallon of grade I costs $3.10 to make, while a gallon of grade Il costs $3.60 to make. The weekly fixed costs are $3950. Step 1 of 2: Find the cost function C(x, y) for making x gallons of grade I and y gallons of grade II.
Find the point of equilibrium for the following supply and demand equations where ? is number of units and ? is the price per unit. Demand: ?=74−0.000030?=74−0.000030q Supply: ?=43+0.000280?=43+0.000280q Number of units for equilibrium = Price per unit at equilibrium =
b. Find the equilibrium quantity.
Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard model requires 5 hours to assemble and 1 hours for finishing touches. The artisan model requires 2 hours to assemble and 4 hours for finishing touches. Based on their current staffing, they can manage a maximum number of assembly hours available is 50 per day, and the maximum number of finishing hours available is 64 per day. Let x = the number of standard model bookcases produced per day and y = the number of artisan model bookcases produced per day. Write the system of inequalities that represents the maximum number of bookcases that can be produced in one day. 0 Graph the system of inequalities, remember to include x >0 and y > 0 in your graph to get full credit. You will need to include four lines. 25 24 VI
Consider a competitive market in which price adjusts to excess demand or supply and firms enter and exit the industry if profits or losses are being made. Price adjusts to excess demand according to dp 0.5(qº – q$) dt Where qº = 30 – 2p is the demand function, qº = 2N is the supply function, p is price, N is the number of firms in the industry and a is the speed of adjustment coefficient. The number of firms adjust according to dN 5 (p 10) dt Derive a system of differential equation to represent this information. Solve the system.
The table below shows the projected values (in millions of dollars) of hardback college textbooks sold in the United States for the years 2007 to 2009. Year Value 2007 4412 C = 2008 4471 2009 4556 (a) Create a system of linear equations for the data to fit the curve y = at² + bt + c, where t is the year and t = 7 corresponds to 2007, and y is the value of the textbooks. = 4412 = 4471 = 4556 (b) Use Cramer's Rule to solve your system. a = b =
Find the production schedule for the technology matrix and demand vector given below:
Find the production schedule for the technology matrix and demand vector given below: 0.1 0.3 0.4 4 A = 0.1 0.2 0.4 D = 5 %3D 0.1 0.1 3 X =
Derive the two expressions for the IS and LM equilibrium relationships respectively. Sketch a graph of the two relationships.
1. Two well-mixed tanks are hooked up so that water with 2 pounds of salt per gallon flows into the first tank, well - mixed water flows out of the second tank, water flows from the first tank to the second tank, and water flows from the second tank to the first tank. All flows are constant. Determine how much water is in each of the two tanks, given if x is the amount of salt in the first tank and y is the amount of salt in the second tank then 3x = -x + y + 30 and 6y' 2x - 3y. The answer should be 45 gallons in the first tank and 30 gallons in the second tank. =