A Semi-Log Scale Graph for Double Trouble

The graph you made of bacteria doubling made a curved line on an arithmetic graph because a population of bacteria doubling every 20 minutes is an exponential function which is non-linear. Arithmetic means counting in constant intervals along a number line. An example is counting 1, 2, 3, 4, etc. or, counting 5, 10, 15, 20 etc. You can count in any interval as long as you are consistent (adding the same amount every time). Exponential data that scientists graph arithmetically makes a curve and is called non-linear (a curve is not a straight line). Here’s a neat trick to turn a curve into a straight line! Today we’ll make a type of logarithmic scale graph of the exponential function of bacteria doubling versus the arithmetic growth of time. Logarithmic means counting exponentially which is how bacteria populations grow. Much of nature behaves non-linearly so scientists often graph exponential data logarithmically to better fit the data to the graph as a straight line. And scientists can derive information using mathematical formulas from straight lines like rates of change for example. Our graph will be a mixture of arithmetic (time) and logarithmic (number bacteria) axes. This is known as a semi-log graph. You will make a semi-log graph of your double trouble bacteria data.

Graph your double trouble bacteria doubling data semi-logarithmically on the semi-log graph paper on the back of this page.

Follow the directions below carefully to make this type of graph!

Label your x axis time in minutes and label it arithmetically. Starting at the origin, label every 4 lines by 20’s (20, 40, 60, etc.). Now label your y axis number of bacteria. Because this is a logarithmic or log axis notice that the line spacing varies because it is logarithmically (exponentially) scaled! The origin on this scale is 100 which is 1. The next thick dark line up is 101 which is 10 and the second thick dark line up is 102 which is 100, and the third thick dark line is 103 which is 1000. Number these thick dark lines and the one above too (what number is it?)!

How to label the other lines on the log scale y axis, READ CAREFULLY!

Label the lines above the origin as follows: 2, 3, 4, 5, 6, 7, 8, and 9.

Label the lines above the thick dark line 10 as follows: 20, 30, 40, 50, 60, 70, 80, and 90.

Label the lines above the thick dark line 100 as follows: 200, 300, 400, 500, 600,700, 800, and 900.

How should you label the next set of lines above? Got it? OK, now label them too!

Now graph the data for the bacteria doubling from your Double Trouble paper. If you graph carefully you should get a straight line! Good luck!