Exponential Growth - An Example of Non-Linear Change

From the Powers of 10 slide show, write down what you saw.

100 m ______

103 m______

106 m ______

109 m______

1012 m______

1016 m ______This distance is 1 ______

1021 m ______How many light years is this? ______

How many years does it take for the Milky Way to spin (revolve)once? ______

10-1 m______

10-3 m______

10-5 m______How many microns? ______

10-6 m ______How many microns? ______

10-7 m______How many microns? ______

10-8 m______How many microns? ______

10-9 m______How many angstroms? _____ How many nanometers? _____

10-14 m______How many picometers? _____ How many fermi’s _____

Distances growing larger or smaller by exponentsare known as exponential growth. Ex: 100, 101, 102, 103, etc. Another example might be 20, 21, 22, etc. A graph of exponential growth is a curve and is called non-linear. Here is an example of an exponential growth graph showing how a population of animalsincreases rapidly (exponentially) over time.

Solve the following problems below to find data points, and then make a graph on the back of this paper of x on the horizontal (bottom) axis and y on the vertical (up) axis.

If x = 1, then y = x2therefore y = ______your1stdata point would be: (x, y) = ( , )

If x = 2, then y = x2 therefore y = ______your 2nd data point would be: (x, y) = ( , )

If x = 3, then y = x2 therefore y = ______your 3rd data point would be: (x, y) = ( , )

If x = 4, then y = x2 therefore y = ______your 4th data point would be: (x, y) = ( , )

If x = 5, then y = x2 therefore y= ______your 5th data point would be: (x, y) = ( , )

How to Make Your Graph: Make your graph carefully, accurately, and neatly for the best grade!

1. Use a ruler to darken the x and y axiswith your pencil. The x axis is the horizontal line at the bottom. The y axis is the vertical line at the far left.

2. Label the x axis, x. Label the y axis, y. Number both axesby one’s to the end of each axis.

3. Make a dot on your graph for each of your data points. Then use your ruler to connect the dots in a straight line.

THOUGHT QUESTION: If you plotted your data points correctly, your graph should have a number of straight lines connected by dots. But if exponential growth graphs have curved lines, how could you make your connected lines a curve? (HINT: Think about what would happen if you plotted new data points between the data points you plotted on your graph.)

Now solve the following problems to find data points and plot another separate line for the powers of 10 slide show on the same graph above. Label this line: line 2

If x = 1, then y = 10x therefore y = ______your 1st data point would be: (x, y) = ( , )

If x = 2, then y = 10x therefore y = ______your 2nd data point would be: (x, y) = ( , )

If x = 3, then y = 10x therefore y = ______your 3rd data point would be: (x, y) = ( , )

If x = 4, then y = 10x therefore y = ______your 4th data point would be: (x, y) = ( ,

If x = 5, then y = 10x therefore y= ______your 5th data point would be: (x, y) = ( , )

What is the obvious problem with trying to graph the powers of 10 slide show points?