Exponential growth and decay by percentage

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  1. exponential growth/decay by percentage

    The population of rabbits is increasing by 70% every 6 months.
    Presently there are 500 rabits. How many years will it take for
    the population to reach 1,000,000?
    1. exponential growth/decay by percentage

      The intensity of light is reduced by 2% for each meter that a diver
      descends below the surface of the water. At what depth is the intensity of
      light only 10% of that at the surface?

      Topic Notes
      Exponential growth/decay rates can be presented in percentages. We will work on questions of this kind in this lesson.
      exponential growth/decay: Af=Ai(f)timeperiod { A_f = A_i (f)^{time\over period}}

      Af {A_f} : final amount
      Ai {A_i} : initial amount
      f {f }
      : growth/decay factor
      half-timef=12 \to f = {1\over 2}
      f=3\to f = {3}
      f=10 \to f = {10}
      increase by 10%f=(1+10100)=1.1 \to f = {({1 + {10\over 100}}) } { = 1.1}
      decrease by 8%f=(18100)=0.92 \to f = {({1 - {8\over 100}}) } { = 0.92}
      time {time} : total time given
      period {period} : every length of time