Question

The study of size and shape is called allometry, and many allometric relationships involve exponents that are tions or decimals. For example, the body measurements of most four-legged animals, from mice to elephants, obey (approximately) the following power law: Average body thickness = 0.4(hip-to-shoulder length)^(3/2). Assuming that this same relationship held for dinosaurs, find the average body thickness of the following dinosaur, whose hip-to-shoulder length was 9 feet.

a) 1.8 feet
b) 3.6 feet
c) 5.4 feet
d) 7.2 feet

Answer 1

The average body thickness of a dinosaur with a hip-to-shoulder length of 9 feet can be calculated using the given power law equation.

Step-by-step explanation:

The study of size and shape, known as allometry, often involves relationships with fractional exponents. In the case of the given example, the average body thickness of most four-legged animals can be estimated using the power law equation: Average body thickness = 0.4 * (hip-to-shoulder length)^(3/2). To find the average body thickness of a dinosaur with a hip-to-shoulder length of 9 feet, we can substitute this value into the equation.

Average body thickness = 0.4 * (9 feet)^(3/2)

Using a calculator, we can evaluate this expression and find that the average body thickness of the dinosaur is 7.2 feet. Therefore, the correct answer is d) 7.2 feet.