Exponential growth and decay by percentage

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

0/2
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?

Topic Notes
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