Exponential growth and decay by a percentage

Get the most by viewing this topic in your current grade. Pick your course now.

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?
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?

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

Exponential growth and decay by percentage