Exponential Growth & Decay Explorer
Compare multiplying and adding growth for bacteria, savings, radioactive decay and viral videos, with a log scale option.
Growth that multiplies keeps getting faster; growth that adds stays steady. Change the starting amount and the percent change each step, choose a real-world story, and switch the graph to a log scale to see exponentials become straight lines.
About the Exponential Growth & Decay Explorer
Free exponential growth & decay explorer. Compare multiplying and adding growth for bacteria, savings, radioactive decay and viral videos, with a log scale option. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for math, the exponential growth & decay explorer runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Compare multiplying and adding growth for bacteria, savings, radioactive decay and viral videos, with a log scale option. Use it to explore math ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Exponential Growth & Decay Explorer
- Use the controls to change Story, Starting amount, Change each step, Number of steps, Graph scale. The simulation reacts instantly.
- Pick an option such as Bacteria, Savings account, Radioactive decay, Viral video to switch modes or load an example.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Choose Bacteria and read the doubling time.
- Set the change to -50 percent and find the half-life.
- Switch to the log scale and see the exponential straighten out.
- Compare 5 percent savings interest with a viral video at 60 percent.
Key ideas you can learn
- Exponential change multiplies by the same factor every step.
- Linear change adds the same amount every step, so exponentials eventually overtake it.
- The doubling time (growth) or half-life (decay) stays the same however large the amount gets.
- On a log scale an exponential graph becomes a straight line.
Where this is used in the real world
Compound interest, population growth, epidemics, radioactive dating, depreciation and computer memory growth all follow exponential patterns.
Who is this simulation for?
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
What is the difference between exponential and linear growth?
Linear growth adds a fixed amount each step. Exponential growth multiplies by a fixed factor, so it speeds up.
How do you find the doubling time?
Doubling time = ln 2 ÷ ln (growth factor).
Is the Exponential Growth & Decay Explorer free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Exponential Growth & Decay Explorer work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.