"he amount of grovth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall.t For a pasture in the arid zone of Australia, the folloving formula gives an approximation of the growth. Y= -55.12 - 0.01535N - 0.00056N + 3.946R tere Ris the amount of rainfall, in millimeters, over a 3-month period, N is the plant biomass, in kilograms per hectare, at the beginning of that period, and Y is the growth, in kilograms per hectare, of the biomass over that period. (For comparison, 100 millimeters is about 3.9 inches, and 100 ilograms per hectare is about 89 pounds per acre.) How ve consider the amount of growth Y as a function of the amount of plant biomass H already present. (a) First ve assume that the rainfall is 80 millimeters, so R= 80. O Find a formula for the growth Y as a function of the amount N of plant biomass already present. ka/ha (i) Make a graph of Y versus N. Include biomass levels N from O to 800 kilograms per hectare. 400 300 v 200 Y 200 100 100 v 200 100 100 0 700 00 (ii) what happens to the amount of growth Y as the amount N of plant biomass already present increases? O The amount of grovth increases. O The amount of grovth decreases. Explain your answer in practical terms.
"he amount of grovth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall.t For a pasture in the arid zone of Australia, the folloving formula gives an approximation of the growth. Y= -55.12 - 0.01535N - 0.00056N + 3.946R tere Ris the amount of rainfall, in millimeters, over a 3-month period, N is the plant biomass, in kilograms per hectare, at the beginning of that period, and Y is the growth, in kilograms per hectare, of the biomass over that period. (For comparison, 100 millimeters is about 3.9 inches, and 100 ilograms per hectare is about 89 pounds per acre.) How ve consider the amount of growth Y as a function of the amount of plant biomass H already present. (a) First ve assume that the rainfall is 80 millimeters, so R= 80. O Find a formula for the growth Y as a function of the amount N of plant biomass already present. ka/ha (i) Make a graph of Y versus N. Include biomass levels N from O to 800 kilograms per hectare. 400 300 v 200 Y 200 100 100 v 200 100 100 0 700 00 (ii) what happens to the amount of growth Y as the amount N of plant biomass already present increases? O The amount of grovth increases. O The amount of grovth decreases. Explain your answer in practical terms.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:The amount of growth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall.t For a pasture in the arid zone of Australia, the following formula gives an approximation of the growth.
Y = -55.12 - 0.01535N - 0.00056N? + 3.946R
Here Ris the amount of rainfall, in millimeters, over a 3-month period, Nis the plant biomass, in kilograms per hectare, at the beginning of that period, and Y is the growth, in kilograms per hectare, of the biomass over that period. (For comparison, 100 millimeters is about 3.9 inches, and 100
kilograms per hectare is about 89 pounds per acre.)
Now we consider the amount of growth Y as a function of the amount of plant biomass N already present.
(a) First we assume that the rainfall is 80 millimeters, so R = 80.
(1) Find a formula for the growth Y as a function of the amount N of plant biomass already present.
kg/ha
(ii) Make a graph of Y versus N. Include biomass levels N from 0 to 800 kilograms per hectare.
300
100
100 200 300 400 500 600 700 BOn
100 200 300 400 500 600 700 no0
N
N
400
400
Y 200
100
100
100 200 300 400 500 600 700 800
100 200 300 400 500 600 700 B00
(iii) What happens to the amount of growth Y as the amount N of plant biomass already present increases?
O The amount of growth increases.
O The amount of growth decreases.
Explain your answer in practical terms.
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Expert Solution
Step 1
Formula for the growth of pasture in the arid zone of Australia :
where is amount of planted biomass
and is the amount of rainfall
(a)To find the formulate of for Amount of rainfall and amount of planted biomass be 'N' itself.
(b)To plot the graph versus for the obtained formula
(c)To find the effect on when amount of biomass is increased
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