Exponential growth and decay by a factor

All in One Place

Everything you need for better grades in university, high school and elementary.

Learn with Ease

Made in Canada with help for all provincial curriculums, so you can study in confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

  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?
    Topic 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-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