One for my maths students ... and my fellow hoarders...

I was pondering about the theory of exponential growth ... like you do of a Tuesday morning.

As a phenomena it can be amazing . Say you bought 3 bunnies and within 2 months you had 18 bunnies. Assuming the growth pattern continues along those lines how many would you end up with a year from now ? ( or for my scrapping followers, say you bought 2 items of stash and within 2 months that had grown to 18 )

Starting with the formula

y(t) = a x ekt   ( where kt is the index ... can't work out how to shift the text up )

where:

y(t) = the amount at time t
a = the amount at the start
k = rate of growth
t = time


If a = 3 bunnies and t = 2 months and today y(2) = 18 bunnies

18 = 3 x e2t

Solving for k :

6 = e2k

Natural logarithm for both sides:

In(6) = In (e2k)

In (ex) = x so:  In (6) =2k

Rearrange

 k = In (6) / 2


So in 2 more months time ( at t = 4 months ) and 1 year from today ( t = 14  months )

y (4) = 3e (in (6)/2 ) x 4 = 108

y(14) = 3e (In(6)/2) x 14 = 839,808

.... which may just explain why the 3 pizza boxes of stash I've acquired in the last 2 months will have grown substantially within a year , assuming they're multiplying like rabbits and more to the point , why it's taken me the best part of 2 months to sort out my hoard of 10 years !