Modifying S-Curve to accept starting value

[kcmuppet]

Hi

This formula, generates a value a point on a S-curve (B13 at this point =1, the first period)

=Peak_value/(1+EXP(-((LN(1/pc_Peak_at_Hypergrowth_start-1)-LN(1/pc_Peak_at_Hypergrowth_end-1))/(Hypergrowth_end-Hypergrowth_start))*
(B13-(LN(1/pc_Peak_at_Hypergrowth_start-1)/((LN(1/pc_Peak_at_Hypergrowth_start-1)-
LN(1/pc_Peak_at_Hypergrowth_end-1))/(Hypergrowth_end-Hypergrowth_start))+Hypergrowth_start))))

It is possible to modify it so that it accepts a starting value (5% in the example below), rather than distributing the values in the example here:

S-Curve modified.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U
1	Starting percentage	5%
2	Peak	100%
3	Hypergrowth starts ~ period	6
4	% of Peak at Hypergrowth start	25%
5	Hypergrowth ends ~ period	10
6	% of Peak at Hypergrowth end point	70%
7
8
9
10
11
12
13	Period:	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
14	Value at point on curve with existing formula:	2.8%	4.5%	7.2%	11.2%	17.0%	25.0%	35.2%	46.9%	58.9%	70.0%	79.1%	86.1%	90.9%	94.2%	96.4%	97.7%	98.6%	99.1%	99.5%	99.7%
15	Desired value with modified formula:	5.0%	?	?	?	?	?	?	?	?	?	?	?	?	?	?	?	?	?	?	?
Sheet1

Cell Formulas
Range	Formula
B14:U14	C14	=Peak_value/(1+EXP(-(( LN(1/pc_Peak_at_Hypergrowth_start-1)- LN(1/pc_Peak_at_Hypergrowth_end-1))/(Hypergrowth_end-Hypergrowth_start))* (C13-( LN(1/pc_Peak_at_Hypergrowth_start-1)/(( LN(1/pc_Peak_at_Hypergrowth_start-1)- LN(1/pc_Peak_at_Hypergrowth_end-1))/(Hypergrowth_end-Hypergrowth_start))+Hypergrowth_start))))
B13:U13	B13	=SEQUENCE(1,20)
B15	B15	=Start_value
Dynamic array formulas.

Named Ranges
Name	Refers To	Cells
Hypergrowth_end	=Sheet1!$B$5	B14:U14
Hypergrowth_start	=Sheet1!$B$3	B14:U14
pc_Peak_at_Hypergrowth_end	=Sheet1!$B$6	B14:U14
pc_Peak_at_Hypergrowth_start	=Sheet1!$B$4	B14:U14
Peak_value	=Sheet1!$B$2	B14:U14
Start_value	=Sheet1!$B$1	B15

(The maths are explained here, but I'm unable to make contact with the originator)

 

[kcmuppet]

I used this approach instead.