General formula for modelling a growth curve AND add new elements at same time

L

LynchB

Hi all
Ok then - I know that heading didn't really make sense so I'll try
again...

Imagine I have a machine which sell widgets
In
Month 1 it'll sell 1 widgets
Month 2 it'll sell 2 widgets
Month 3 it'll sell 2 widgets
Month 4 it'll sell 5 widgets etc. until after 9 months it reaches the
top of its curve and will sell 21 widgets a month for ever more. The
values are variables and can be changed in a little table area
Now I can easily enough define a table and formula which can model that
by just laying out 1,2,2,5...21 in a table and picking up the correct
value as the formulae trundle along.
However I'd like also to be able to 'what-if' the number of machines
so for example in Mth1 I buy 1 machine, it is also in month 1 of its
curve. In month 2 I add a 2nd machine. Machine 1 is now in month 2 of
its curve and machine 2 is in month 1 of its curve. In month 3 I do
nothing so that machine 1 is in month 3 of its curve and machine 2 is
in month 2 of its curve. In month 4 I add a new machine so that machine
1 is in month 4 of its curve, machine 2 is in month 3 and this new
machine is in month 1 etc. etc Then I might change my mind and decide
not buy the 3rd machine until Month 6 with the inevitable impact on
total widgets sold for the year.

Any thoughts (formulae would be even better ;-)) on a nice generalised
formula that I can apply across all 60 months (doing a 5 year plan
here) which will allow me to plug any combination of numbers of
machines in any combinataion of month. This problem is surely too
common not to have been tackled before no?
Thanks for taking the time to read this rambling and badly explained
post
Cheers
Kinch
 

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