Exponential growth and decay by a factor

Exponential growth and decay by a factor

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.

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.
    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?