# Exponential growth and decay by percentage

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### Examples

#### Lessons

1. exponential growth/decay by percentage

The population of rabbits is increasing by 70% every 6 months.
Presently there are 500 rabits. How many years will it take for
the population to reach 1,000,000?
1. exponential growth/decay by percentage

The intensity of light is reduced by 2% for each meter that a diver
descends below the surface of the water. At what depth is the intensity of
light only 10% of that at the surface?

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###### Topic Basics
Exponential growth/decay rates can be presented in percentages. We will work on questions of this kind 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