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If A' growth rate of number of bacteria at any time t is proportional to number present at any time t and doubles in 1 week than bacteria after four week is

  • A.4A(t)
  • B.24A(t)
  • C.16A(t)
  • D.0.099A(t)

Answer: C

Growth proportional to the amount present gives exponential growth, and doubling every week means the population multiplies by 2 each week.

\[ A(4) = A_{0} \times 2^{4} = 16\,A_{0} \]

The doublings compound rather than add: four weeks give \( 2 \times 2 \times 2 \times 2 = 16 \) times, not \( 2 \times 4 = 8 \) times.

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