Sign In
Sign Up
flag-us

Exponential growth and decay by a factor

Get the most by viewing this topic in your current grade. Pick your course now.

Now Playing:Exponential growth and decay by a factor– Example 1
Examples
  1. triple growth
    A certain type of bug can triple its population every 10 years.
    How many bugs will there be in 50 weeks if there are 76 bugs today?
    Solving exponential equations using exponent rules
    Jump to:NotesPrerequisitesRelated
    Notes
    The growth/decay factor "(1+r)" dictates the rate of exponential growth and decay. We will work on questions related to growth/decay factor 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-time→f=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=(1−8100)=0.92 \to f = {({1 - {8\over 100}}) } { = 0.92}
    time {time} : total time given
    period {period} : every length of time