What do exponential growth and decay have in common?
February 20th, 2023
They both work with the same equation: ##N=B*g^t##
Where
##N=## new situation
##B=## begin
##g=## growth factor
##t=## time
If the growth-factor is greater than ##1##, then we have a growth.
If it is less than ##1## we call it decay.
(if ##g=1## nothing happens, a stable situation)
Examples:
(1) A population of squirrels, starting at 100, grows by 10% every year. Then ##g=1.10## and the equation becomes: ##N=100*1.10^t## with ##t## in years.
(2) A radio-active material with original activity of 100, decays by 10% per day. Then ##g=0.90## (because after a day only 90% will be left) and the equation will be: ##N=100*0.90^t## with ##t## in days.