Exponential growth and decay by percentage

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

  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