Graphing exponential growth

When graphing exponential growth, it is always a good idea to make a table of values and you could look for at least 5 points that you can use to make the graph.

It is also a good idea to choose both negative and positive values for x, especially numbers that are opposites. For example, notice how we chose x = -2 and x = 2.

Graph y = 3 × 2x

x
3×2x
(x, y)
-2
3×2-2 = 3 / 22 = 3/4
(-2, 3/4)
-1
3×2-1 = 3 / 21 = 3/2
(-1, 3/2)
0
3×20 = 3 × 1 = 3
(0, 3)
1
3×21 = 3 × 2 = 6
(1, 6)
2
3×22 = 3 × 4 = 12
(2, 12)
Graph of an exponential growth

Did you make the following observations about the figure above?

  • Each square in vertical axis or y-axis represents 1 unit.
  • Each square in horizontal axis or x-axis represents 1 unit.

Important observation when graphing exponential growth


Now, let us see what will happen if we choose the following values for x:

x = -4, -10, -20

If x = -4, y = 3 × 2-4 = 3 / 24 = 3 / 16 = 0.1875.

If x = -10, y = 3 × 2-10 = 3 / 210 = 3 / 1024 = 0.00292968.

If x = -20, y = 3 × 2-20 = 3 / 220 = 3 / 1048573 = 0.00000286.

As the values of x get smaller and smaller, the values of y get smaller and smaller as well. Notice that these the values of y will get closer and closer to 0.

Now, let us see what will happen if we choose the following values for x:

x = 4, 10, 20

If x = 4, y = 3 × 24 = 3 × 24 = 3 × 16 = 48.

If x = 10, y = 3 × 210 = 3 × 210 = 3 × 1024 = 3072.

If x = 20, y = 3 × 220 = 3 × 220 = 3 × 1048576 = 3145728.

As the values of x get bigger and bigger, the values of y get bigger and bigger as well. Notice that these the values of y will approach infinity.

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