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.

Recent Articles

  1. Quadratic Formula: Easy To Follow Steps

    Jan 26, 23 11:44 AM

    Quadratic formula
    Learn about the quadratic formula, the discriminant, important definitions related to the formula, and applications.

    Read More

  2. Area Formula - List of Important Formulas

    Jan 25, 23 05:54 AM

    Frequently used area formulas
    What is the area formula for a two-dimensional figure? Here is a list of the ones that you must know!

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes