How to Use Population Growth Calculator

Exponential Growth

• Initial Population (P₀) ⓘ — e.g., 1000
• Growth Rate (%) ⓘ — e.g., 5
• Time Period ⓘ — e.g., 10
• Final Population (Pₜ) ⓘ

How to use (4 short steps)

1. Select the Exponential Growth model.
2. Enter the Initial Population (P₀), the Growth Rate (%), and the Time Period (t).
3. Apply the formula:
   Pt=P0×(1+r100)tP_t = P_0 \times \big(1 + \dfrac{r}{100}\big)^tPt​=P0​×(1+100r​)t
4. Read the Final Population (round if you need whole individuals).

Quick example

Inputs: P₀ = 1000, r = 5%, t = 10

Math breakdown (step-by-step):

• Growth factor = 1+5100=1.051 + \tfrac{5}{100} = 1.051+1005​=1.05
• Raise to the 10th power by repeated multiplication:
  1.05² = 1.1025
  1.05³ = 1.157625
  1.05⁴ = 1.21550625
  1.05⁵ = 1.2762815625
  1.05⁶ = 1.340095640625
  1.05⁷ = 1.40710042265625
  1.05⁸ = 1.4774554437890625
  1.05⁹ = 1.5513282159785156
  1.05¹⁰ = 1.628894626777442

Final population:
P10=1000×1.628894626777442=1628.894626777442≈1629P_{10} = 1000 \times 1.628894626777442 = 1628.894626777442 \approx 1629P10​=1000×1.628894626777442=1628.894626777442≈1629

(Round to the nearest whole number if modeling people; keep decimals for continuous quantities like bacteria or money.)

Information is collected from Worldometer