Thinking with Mathematical Models Unit Review Part 2
1.
Scientists are interested in finding out how different species adapt to finding food sources. One group studied crocodilian
species to find out how their bite force was related to body mass and diet. The table below displays the information they
collected on body mass (in pounds) and bite force (in pounds).
Species
Dwarf crocodile
Crocodile F
Alligator A
Caiman A
Caiman B
Caiman C
Croc A
Nile crocodile
Croc B
Croc C
Croc D
Caiman D
Indian Gharial croc
Crocodile G
American croc
Croc D
Croc E
American Alligator
Alligator B
Alligator C
Body Mass (pounds)
35
40
30
28
37
45
110
275
130
135
135
125
225
220
270
285
425
300
325
365
Bite Force (pounds)
450
260
250
230
240
255
550
650
500
600
750
550
400
1,000
900
750
1,650
1,150
1,200
1,450
Data Source: PLoS One Greg Erickson biomechanics, Florida State University
Construct a scatter plot of body mass (𝑥) and bite force (𝑦). Use the grid below, and be sure to add an appropriate scale to the
axes.
2.
Do you think that there is a statistical relationship between body mass and bite force? If so, describe the nature of the
relationship.
Sample response: Yes, because it looks like there is an upward pattern in the scatter plot. It appears that alligators with larger
body mass also tend to have greater bite force.
3.
Based on the scatter plot, can you conclude that increased body mass causes increased bite force? Explain.
Sample response: No. Just because there is a statistical relationship between body mass and bite force does not
mean that there is a cause-and-effect relationship.
4.
When there is a car accident how do the investigators determine the speed of the cars involved? One way is to measure the
skid marks left by the car and use this length to estimate the speed.
The table below shows data collected from an experiment with a test car. The first column is the length of the skid mark (in
feet) and the second column is the speed of the car (in miles per hour).
Skid-Mark Length (𝐟𝐭.)
5
17
65
105
205
265
Speed (𝐦𝐩𝐡)
10
20
40
50
70
80
a.
Construct a scatter plot of speed versus skid-mark length on the grid below.
b.
The relationship between speed and skid-mark length can be described by a curve. Sketch a curve through the data that
best represents the relationship between skid-mark length and speed of the car. Remember to draw a smooth curve that
does not just connect the ordered pairs.
See above
c.
If the car left a skid mark of 60 ft., what is an estimate for the speed of the car? Explain how you determined the estimate.
Approximately 38 mph. Using the graph, for a skid mark of 65 ft. the speed was 40 mph, so the estimate is slightly less than
40 mph.
d.
A car left a skid mark of 150 ft. Use the curve you sketched to estimate the speed at which the car was traveling.
𝟔𝟐. 𝟓 𝐦𝐩𝐡
e.
If a car leaves a skid mark that is twice as long as another skid mark, was the car going twice as fast? Explain.
No, when the skid mark was 105 ft. long, the car was traveling 50 mph. When skid mark was 205 ft. long (about twice
the 105 ft.), the car was traveling 70 mph, which is not twice as fast.