posted by mysterychicken on .
1. Exponential growth follows the formula y=a(1+r)^x and exponential decay follows the formula y=a(1-r)^x..
This seems obviously TRUE
But now I'm having doubts about the decay formula
Is this true or false?
Normally exponential growth is expressed as
f(t) = a e^kt
and exponential decay is
f(t) = a e^-kt
If 0<r<1, then the statement is true, since then we have
1-r < 1 so we have a fraction, and exponential of a fraction is e^-kt for some k.
With no restrictions on r, things get a bit dicier.
I think in your case, say you have a 12% growth rate. Then
f(x) = a(1.12)^x
At 12% decay rate would then mean that 88% is left after each interval, so you would indeed have
f(x) = a(1-.12)^x = a(.88)^x