Example of Exponential Growth: Explained Simply

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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