What Is Exponential Growth?
Exponential growth occurs when a quantity increases by a fixed percentage or factor over regular intervals. This results in the quantity growing faster and faster as time passes.
Simple Exponential Growth Example
Imagine you have $100 in a savings account with an annual interest rate of 5% compounded yearly.
- After 1 year, the amount grows to:
100×1.05=105100 \times 1.05 = 105100×1.05=105 dollars. - After 2 years, it grows to:
105×1.05=110.25105 \times 1.05 = 110.25105×1.05=110.25 dollars. - After 3 years:
110.25×1.05=115.76110.25 \times 1.05 = 115.76110.25×1.05=115.76 dollars.
The formula for the amount after nnn years is:
A=P×(1+r)nA = P \times (1 + r)^nA=P×(1+r)n
where:
- AAA = amount after nnn years
- PPP = initial principal ($100)
- rrr = growth rate (5% or 0.05)
- nnn = number of years
Real-World Applications of Exponential Growth
- Population growth where birth rates lead to increasing numbers over time.
- Spread of viruses in epidemiology during outbreaks.
- Investment growth in finance with compound interest.
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