# Exponential growth and decay by a factor

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##### Examples
###### Lessons
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: ${ A_f = A_i (f)^{time\over period}}$

${A_f}$: final amount
${A_i}$: initial amount
${f }$
: growth/decay factor
half-time$\to f = {1\over 2}$
triple
$\to f = {3}$
ten-fold
$\to f = {10}$
increase by 10%$\to f = {({1 + {10\over 100}}) } { = 1.1}$
decrease by 8%$\to f = {({1 - {8\over 100}}) } { = 0.92}$
${time}$ : total time given
${period}$ : every length of time