Facts from the Page (Exponential Population Growth)

• Population growth can occur when resources like food and space are unlimited.
• Under ideal conditions, population shows exponential growth.
• The increase depends on:
  • Birth rate (b)
  • Death rate (d)

Example values of $r$r:

• Norway rat → 0.015
• Flour beetle → 0.12
• Human population → 0.16

Any species can grow exponentially for some time if resources are unlimited. Exponential growth produces a J-shaped curve. In the graph:

• $K$represents carrying capacity.

Population cannot grow indefinitely in nature because environmental resistance and limited resources act as checks.

Facts from the “King and Wheat” Story

• A king offered a reward to a wise man.
• The wise man asked for wheat grains on a chessboard:
  • 1 grain on first square
  • 2 on second
  • 4 on third
  • doubling on every next square
• Total squares on chessboard = 64.
• The number of grains increased enormously.
• The king’s entire kingdom could not supply so much wheat.
• This story demonstrates:
  • Exponential increase
  • Population can grow rapidly under unlimited conditions
  • Resources eventually become insufficient