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Exponential growth and decay by a factor

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Now Playing:Exponential growth and decay by a factor– Example 1
Examples
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  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?

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    Exponential growth and decay by a factor
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    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