Definition
Exponential growth
Exponential growth means multiplying a positive quantity by the same factor over equal steps.
Continue from this idea into connected AXIO math.
Defining relationship
Same step, same multiplier. Exponential growth does not add the same amount each time.
Exponential growth is growth in which a positive quantity is multiplied by the same constant factor greater than 1 whenever the input increases by equal amounts.
- × 2
- × 2
- × 2
- × 2
The multiplier stays fixed; the amount added does not.
What it means
Look at what happens from one step to the next. If the quantity is multiplied by the same number each time, it has exponential growth. The increases get larger because they are built from an ever-growing amount.
Remember it
Same step, same multiplier. Exponential growth does not add the same amount each time.
Example
Start with 3 and double at each step: 3, 6, 12, 24, 48. Four equal steps use the multiplier 2, so the last value is 3 × 2⁴ = 48.
Watch for
The pattern 3, 6, 9, 12 adds 3 each time. That is linear growth, not exponential growth.
Common mix-up
Fast or large growth is not automatically exponential. The same multiplicative factor must repeat over equal input intervals.
Exact meaning
Exponential growth is growth in which a positive quantity is multiplied by the same constant factor greater than 1 whenever the input increases by equal amounts.