Page 34 - Laboratory Manual in Physical Geology

Rates Involving Time Graphing Relationships
The most common kind of rate is an expression of how Graphs are useful for visualizing relationships in your
something changes per unit of time, such as miles per data. So before you can make a graph, you need a set
hour. For example, if you drive 100 miles in 2 hours, then of data. Data makes more sense if you organize it into a
your rate of travel is 100 miles ÷ 2 hours, or 50 miles per chart. If you use Excel™, then your chart of data is called a
hour (50 mi/h or 50 MPH). spreadsheet. When organizing data, scientists normally have
■ Knowing the rate of change per unit of time enables a column of data representing an independent variable.

you to predict (calculate) how much change will occur The independent variable is what you control, to see how
by a future time. For example, if your rate of travel is it affects the dependent variable. The dependent variable is
50 mi/h, then how far will you travel in four hours? the variable being tested for, so you do not know what the
values will be until you do an experiment. As you change
50 mi 4 h the independent variable, you do a test or experiment
* = 200 mi to observe and record the dependent variable data. For
1 h 1
example, if you want to characterize how fast a plant grows,

■ Knowing the rate of change per unit of time also then you may decide to measure its height every week (time
enables you to predict (calculate) how long it will take here being the independent variable). When you measure
for a given amount of change to occur. If your rate of and record the plant’s height every week, then you are
travel is 50 mi/h, then how far will it take you to travel recording the dependent variable data. Geologists often
400 miles? want to characterize how something changes over time, so
time is usually the independent variable. If you are placing
400 mi
= 8 h your data in an Excel™ spreadsheet, then the independent
50 mi>h variable data are entered in the first column (left-hand
column, column A). The dependent variable data are
Calculating Rates—The Math You Need entered in column B. Once you have an organized chart of
You can learn more about calculating rates data, then you can use it to construct a graph.
(including practice problems) at this site X-Y graphs are graphs with two axes, a horizontal
featuring The Math You Need, When You X-axis and a vertical Y-axis. Scientists universally plot the
Need It math tutorials for students in independent variable along the X-axis and the dependent
introductory geoscience courses: http:// variable on the Y-axis. In Excel™, X-Y graphs are called
serc.carleton.edu/ mathyouneed/rates/ scatter graphs or line graphs.
index.html ■ Scatter graphs are X-Y graphs on which points are
plotted (paced on the graph) but not joined into a line.
Density: Mass per Volume Picture holes in a dart board. They are like the points
Every material has a mass that can be weighed and on a scatter plot. By analyzing relationships among the
a volume of space that it occupies. However, the points you can determine if they are widely scattered
relationship between a material’s mass and volume (a weak relationship to one another or no relationship at
tends to vary from one kind of material to another. all) or closely concentrated (a strong relationship to one
For example, a bucket of rocks has much greater mass another). You can also look for patterns in the graph such
than an equal-sized bucket of air. Therefore a useful as whether or not the points form one concentration or
way to describe an object is to determine its mass per two or three concentrations of related points.
unit of volume, which is a rate called density . Per
■ Line graphs are X-Y graphs on which points are
refers to division (as in miles per hour). So, density
plotted and joined to form a line. If the points form a
is a measure (rate) of an object’s mass divided by its
line that runs from lower left to upper right, then
volume (density = mass , volume). Scientists and
there is what is called a positive or direct relationship .

mathematicians use the Greek character rho ( r) to
This means that as the values of X (independent
represent density. Also, the gram (g) is the basic metric
variable) increase, so do the values of Y. If the points
unit of mass, and the cubic centimeter is the basic form a line that runs from upper left to lower right,
3

unit of metric volume (cm ), so density ( r) is usually then there is what is called a negative or inverse

3
expressed in grams per cubic centimeter (g>cm ).

relationship . This means that as the values of X
(independent variable) increase, so do the values of Y.
Calculating Density—The Math You Need In both cases just described, the closer the points are
You can learn more about calculating den- to the line, the stronger is the relationship. Also, some
sity (including practice problems) at this line graphs compare two kinds of dependent variables
site featuring The Math You Need, When to the independent variable. For example, you may
You Need It math tutorials for students in want to know how plant height and number of leaves
introductory geoscience courses: http:// vary over the same time intervals. By plotting the data
serc.carleton.edu/mathyouneed/ density/ (two sets of dependent variable data) against the time
index.html
Thinking Like a Geologist ■ 19