School

University of MarylandDepartment

Government and PoliticsCourse Code

GVPT 100Professor

Irwin MorrisStudy Guide

FinalThis

**preview**shows page 1. to view the full**5 pages of the document.**BSCI 207 Spring, 2019

Homework #2: Scaling

Please type your answers into this document and upload to ELMS by

11:59 P.M., Monday, February 18

Also on ELMS: some time on Sunday (February 17) or Monday (February 18) take

a short timed quiz on Scaling

You may work on this homework on your own or discuss it with others. If you work through

questions with others, be sure to turn in your own work, at the level at which you understand it.

Do not simply copy answers from or for someone else. Questions such as these may show up on

quizzes or exams, so be sure to work to understand how to arrive at the answers.

Note: Questions or statements in italics require a response from you.

Problem 1. Fish scaling

You have caught eight individuals of a particular fish species and measured the length, depth (vertical

height), and thickness (side-to-side distance) of each. For each fish, approximate total surface area and

volume of each fish were calculated, as shown in the table below.

LENGTH (cm)

THICKNESS (cm)

DEPTH (cm)

VOLUME (cm3)

AREA (cm2)

2

0.5

1

1

6

4

1

2

8

24

6

1.5

3

27

54

10

2.5

5

125

150

16

4

8

512

384

24

6

12

1728

864

48

12

24

13824

3456

60

15

30

27000

5400

Use Excel (or a similar program) to fit power functions (scaling equations, Y=axb) to these data (a

power function, which has the form y = axb, has a variable base raised to a fixed exponent). Exactly

how to do this will depend on your version of Excel. But the procedure will be something like this:

1. Select the two columns of numbers you wish to plot (e.g., depth and volume).

2. Click on the Charts tab [or Insert tab] & select Scatter plot [X Y scatter]

3. Select the resulting plot and click on the Chart Layout tab & Trendline subtab [Add chart

element, then Trendline]

4. Under Trendline Options, select Power [possibly under More trendline options] & under

Options (just to the left) [or under Format Trendline] click on “Display equation on chart”

and click OK.

The equation of the power function fitted to your data should be displayed on your graph.

1a) (1/4 pt) What is the value of b for depth vs. volume (note that “A versus B” tells you that A is

on the Y axis and B is on the X axis)? Paste your graph below.

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1b) (1/4 pt) What is the value of b for area vs. volume? Paste your graph below.

1c) (1/4 pt) What is the value of b for volume vs. area? Paste your graph below.

1d) (1/4 pt) What is the value of b for thickness vs. area? Paste your graph below.

1e) (1/4 pt) Do your fish appear to be growing isometrically or allometrically? Explain.

Problem 2. Dinosaur scaling

Theropod Dinosaur Species

Body Mass (kg)

Body Length (m)

Staurikosaurus pricei

19

2.08

Coelophysis bauri

15.3

2.68

Coelophysis rhodesiensis

13

2.15

Elaphrosaurus bambergi

210

6.2

Liliensternus liliensterni

127

5.15

Dilophosaurus wetherilli

283

6.03

Ceratosaurus nasicoris

524

5.69

Eustreptospondylus oxoniensis

218

4.63

Metriacanthosaurus? sp.

130

3.8

Allosaurus fragilis

1010

7.4

Allosaurus atrox

1320

7.9

Gorgosaurus libratus

700

5.8

Gorgosaurus libratus

2500

8.6

Daspletosaurus torosus

2300

9

Tarbosaurus bataar

760

5.8

Tarbosaurus bataar

2100

7.7

Tyrannosaurus rex

5700

10.6

Deinonychus antirrhopus

45

3.06

Deinonychus antirrhopus

73

3.43

Velociraptor mongoliensis

15

2.07

Ornithomimus edmontonicus

110

3.3

Ornithomimus brevitertius

144

3.66

Gallimimus bullatus

27

2.15

Gallimimus bullatus

440

6

The dinosaur data above were plotted in Excel, as shown below

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