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).

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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...

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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

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