Exponential growth and decay by percentage

Exponential growth and decay by percentage

Exponential growth/decay rates can be presented in percentages. We will work on questions of this kind in this lesson.

Lessons

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}
triple
f=3\to f = {3}
ten-fold
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
  • 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?

  • 2.
    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?