Exhibit 4-3 Paleontology, the Study of Forms of Prehistoric Life, Can Sometimes

question 5

Essay

Exhibit 4-3
Paleontology, the study of forms of prehistoric life, can sometimes be aided by modern biology. The study of prehistoric birds depends on fossil information, which typically consists of imprints in stone of a prehistoric creature's remains. To study the productivity of an ancient ecosystem it would be useful know the actual mass of the individual birds, but this information is not preserved in the fossil record. It seems reasonable that the biomechanics of birds operates much the same today as in the past. For example, relationship between the wing length and total weight of a bird should be very similar today to the relationship in the distant past. The wing lengths of ancient birds are readily obtainable from the fossil record, but the weight is not. Assuming similar biomechanical development for ancient birds and modern birds, a regression model expressing the relationship between wing length and total weight of a modern bird could be used to estimate the mass of similar prehistoric birds and thus gauge some aspects of the ancient ecosystem.
Data is available for some modern birds of prey. Specifically, data on the mean wing length and mean total weight of species of hawk-like birds of prey is given below.
-Refer to Exhibit 4-3. Approximately what proportion of the variability in weight is explained by the wing length?

Develop the ability to round numerical answers to a specified degree of accuracy.

Apply mathematical reasoning to determine the bounds within which a geometric dimension must lie.

Understand the concept of horizontal asymptotes for exponential functions.

Match exponential functions with their corresponding graphs.