Self-thinning: When seeds of a plant are sown at high density in a plot, the seedlings must compete with each other. As time passes, individual plants grow in size, but the density of the plants that survive decreases.33 This is the process of selfthinning. In one experiment, horseweed seeds were sown on October 21, and the plot was sampled on successive dates. The results are summarized in Table 5.8, which gives for each date the density p, in number per square meter, of surviving plants and the average dry weight w, in grams, per plant.
a. Explain how the table illustrates the phenomenon of self-thinning.
b. Find a formula that models w as a power function of p.
c. If the density decreases by a factor of 1 2 , what happens to the weight?
d. The total plant yield y per unit area is defined to be the product of the average weight per plant and the density of the plants: y = w × p. As time goes on, the average weight per plant increases while the density decreases, so it’s unclear whether the total yield will increase or decrease. Use the power function you found in part b to determine whether the total yield increases or decreaseswith time. Check your answer using the table.