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 × 2^x

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)

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.

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.