Growth and decay
Does something grow by the same number each time, or by the same percentage? See the difference on the graph — it gets big.
Your numbers
Answer
After 20 periods (percentage)
2,653.3
After 20 periods (linear)
2,000
Growth factor a
1.05
Doubling time
14.21 periods
How to work it out
- 1a = 1 + 5/100 = 1.05
- 2y = b · aˣ = 1,000 · 1.05^20 = 2,653.3
- 3y = b + k · x = 1,000 + 50 · 20 = 2,000
- 4T₂ = log(2) / log(1.05) = 14.21
The formula
y = b · aˣ, a = 1 + r
Percentage growth: each period is multiplied by the same factor.
y = b + k · x
Linear growth: the same number is added each period.
T₂ = log 2 / log a
The doubling time depends only on the percentage — not on the starting value.
Table
| Period | Percentage | Linear |
|---|---|---|
| 0 | 1,000 | 1,000 |
| 1 | 1,050 | 1,050 |
| 2 | 1,102.5 | 1,100 |
| 3 | 1,157.63 | 1,150 |
| 4 | 1,215.51 | 1,200 |
| 5 | 1,276.28 | 1,250 |
| 6 | 1,340.1 | 1,300 |
| 7 | 1,407.1 | 1,350 |
| 8 | 1,477.46 | 1,400 |
| 9 | 1,551.33 | 1,450 |
| 10 | 1,628.89 | 1,500 |
| 11 | 1,710.34 | 1,550 |
| 12 | 1,795.86 | 1,600 |
| 13 | 1,885.65 | 1,650 |
| 14 | 1,979.93 | 1,700 |
| 15 | 2,078.93 | 1,750 |
| 16 | 2,182.87 | 1,800 |
| 17 | 2,292.02 | 1,850 |
| 18 | 2,406.62 | 1,900 |
| 19 | 2,526.95 | 1,950 |
| 20 | 2,653.3 | 2,000 |
More: Equations and functions
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- Scale and ratiosFrom drawing to reality, the rule of three and dividing in a ratio.
- Two equations with two unknownsSolve a system of equations step by step and see the intersection on the graph.