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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) 2 g of nitrogen. Assume also that in one day they pass 60% of their free nitrogen to the plant, and they use up 30% of this nitrogen for growth. In the plant, 80% 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. В. C. O A. 2.0 2.0 0.6х, 2.0 2.0 0.6х 0.8x1 0.3x 0.8x. 2.0 0.3x1 0.8x2 0.3x1 0.8x2 0.6x, 0.6x2 0.3 0.6 (b) Write down a system of differential equations for x, (t) and x2 (t). dx1 dt dx2 dt

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) 2 g of nitrogen. Assume also that in one day they pass 60% of their free nitrogen to the plant, and they use up 30% of this nitrogen for growth. In the plant, 80% 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. В. C. O A. 2.0 2.0 0.6х, 2.0 2.0 0.6х 0.8x1 0.3x 0.8x. 2.0 0.3x1 0.8x2 0.3x1 0.8x2 0.6x, 0.6x2 0.3 0.6 (b) Write down a system of differential equations for x, (t) and x2 (t). dx1 dt dx2 dt

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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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) 2 g of nitrogen. Assume also that in one day they pass 60% of their free nitrogen to the plant, and they use up 30% of this nitrogen for growth. In the plant, 80% 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. В. C. O A. 2.0 2.0 0.6х, 2.0 2.0 0.6х 0.8x1 0.3x 0.8x. 2.0 0.3x1 0.8x2 0.3x1 0.8x2 0.6x, 0.6x2 0.3 0.6 (b) Write down a system of differential equations for x, (t) and x2 (t). dx1 dt dx2 dt
Transcribed Image Text: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) 2 g of nitrogen. Assume also that in one day they pass 60% of their free nitrogen to the plant, and they use up 30% of this nitrogen for growth. In the plant, 80% 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. В. C. O A. 2.0 2.0 0.6х, 2.0 2.0 0.6х 0.8x1 0.3x 0.8x. 2.0 0.3x1 0.8x2 0.3x1 0.8x2 0.6x, 0.6x2 0.3 0.6 (b) Write down a system of differential equations for x, (t) and x2 (t). dx1 dt dx2 dt
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