More on plant growth: This is a continuation. 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 100 millimeters, so R = 100.
i. Find a formula for the growth Y as a function of the amount N of plant biomass already present.
ii. Make a graph of Y versus N. Include biomass levels N from 0 to 800 kilograms per hectare.
iii. What happens to the amount of growth Y as the amount N of plant biomass already present increases? Explain your answer in practical terms.
b. Next we assume that the rainfall is 80 millimeters, so R = 80.
i. With this lower rainfall level, find a formula for the growth Y as a function of the amount N of plant biomass already present.
ii. Add the graph of Y versus N for the lower rainfall to the graph you found in part a.
iii. According to the graph you just found, what is the effect of lowered rainfall on plant growth? Is your answer consistent with that in part c?