Exponential Graphs
An exponential graph shows a quantity that multiplies by a fixed factor over equal steps, rising or falling rapidly.
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Play with the controls to see the idea in action.
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An exponential graph shows a quantity that multiplies by a fixed factor over equal steps, rising or falling rapidly.
- y equals a to the x passes through (0, 1)
- Growth when a is greater than 1
- Decay when a is between 0 and 1
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Exponential Graphs?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Exponential Graphs. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Exponential Graphs in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Exponential Graphs gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Exponential Graphs in detail
An exponential graph has the form y = aˣ (or y = kaˣ), where the variable is in the power. For a > 1 the curve rises slowly at first and then very steeply, passing through (0, 1), and it never touches the x-axis, which is an asymptote. For 0 < a < 1 it decays towards zero.
Exponential graphs model growth and decay in which the rate of change is proportional to the current size: compound interest, population growth, bacterial culture, radioactive decay and cooling. Comparing them with linear graphs shows why exponential growth eventually outpaces steady increases.
How the interactive helps you understand Exponential Graphs
Watch the growth curve in the interactive. Use any sliders or buttons it offers to change the values and see how the growth curve responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Exponential Graphs.
Real-life uses and examples
- Use Exponential Graphs when comparing prices, discounts or recipe quantities in everyday life.
- Explain Exponential Graphs to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Exponential Graphs in exam questions, where it often sits inside a short word problem.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Exponential Graphs.
- Memorising the steps for Exponential Graphs without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Exponential Graphs
What is Exponential Graphs?
An exponential graph shows a quantity that multiplies by a fixed factor over equal steps, rising or falling rapidly.
What are the most important points about Exponential Graphs?
The main points are: y equals a to the x passes through (0, 1); Growth when a is greater than 1; Decay when a is between 0 and 1.
Why is Exponential Graphs useful?
Understanding Exponential Graphs gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Exponential Graphs?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Exponential Graphs?
Related topics in Mathematics include Speed-Time Graphs, Angles on Lines and Points, Types of Triangle.