HP 20S and DM 42 Learning Curve
The Learning Curve
The learning curve relates the average time it takes to produce, finished, or manufacture a certain amount of units using two factors: (1) the tie it takes to complete a first product or procedure and (2) a learning curve percentage. Typically the learning curve percentage is determined by the fraction of a time it takes to complete a second product or procedure.
For example: If it takes 3 hours to manufacture and assemble the first desk, and it only takes 2.5 hours to a second desk, the learning curve is 2.5 ÷ 3 or about 0.8333 (83.33%).
The learning curve formula is:
y = a * x^b
where:
b: The learning curve index, where b = log f ÷ log 2. f is the learning curve.
a: The time to finish a first product
x: how many products needed to achieve an average time per products
y: the average time per product
HP 20S: Learning Curve
Input Registers:
R1: a
R2: f
Output Registers:
R3: b
Input/Output Registers:
R4: x
R5: y
Labels:
Initialize a and f: a [ INPUT ] f [ XEQ ] (A) (view b)
Given x, calculate y: x [ XEQ ] (B)
Given y, calculate x: y [ XEQ ] (C)
Code:
LBL A; 01 61, 41, A
STO 2; 02 21, 2
SWAP; 03 51, 31
STO 1; 04 21, 1
SWAP; 05 51, 31
LOG; 06 51, 13
÷ ; 07 45
2 ; 08 2
LOG; 09 51, 13
= ; 10 74
STO 3; 11 21, 3
RTN; 12 61, 26
LBL B; 13 61, 41, b
STO 4; 14 21, 4
y^x; 15 14
RCL 3; 16 22, 3
× ; 17 55
RCL 1; 18 22, 1
= ; 19 74
STO 5; 20 21, 5
RTN; 21 61, 26
LBL C; 22 61, 41, C
STO 5; 23 21, 5
( ; 24 33
RCL 5; 25 22, 5
÷ ; 26 45
RCL 1; 27 22, 1
) ; 28 34
LOG; 29 51, 13
÷ ; 30 45
RCL 3; 31 22, 3
= ; 32 74
10^x; 33 51, 12
STO 4; 34 21, 4
RTN; 35 61, 26
DM42: Learning Curve
Input Registers:
R01: a
R02: f
Output Registers:
R03: b
Input/Output Registers:
R04: x
R05: y
Code:
00 {92-Byte Prgm}
01 LBL “LEARN”
02 LBL 11
03 “A,B>”
04 KEY 1 GTO 01
05 “X>Y”
06 KEY 2 GTO 02
07 “Y>X”
08 KEY 3 GTO 03
09 “EXIT”
10 KEY 6 GTO 06
11 MENU
12 LBL 10
13 STOP
14 GTO 10
15 LBL 01
16 STO 02
17 x<>y
18 STO 01
19 x<>y
20 LOG
21 2
22 LOG
23 ÷
24 STO 03
25 LBL 11
26 LBL 02
27 STO 04
28 RCL 03
29 Y↑X
30 RCL× 01
31 STO 05
32 GTO 11
33 LBL 03
34 STO 05
35 RCL÷ 01
36 LOG
37 RCL 03
38 1/x
39 ×
40 10↑X
41 STO 04
42 GTO 11
43 LBL 06
44 CLMENU
45 EXITALL
46 RTN
(47 END)
Examples
(FIX 4)
Example 1:
a = 15, f = 0.8
Input: x = 20, Result: y ≈ 5.7181
Input: x = 40, Result y ≈ 4.5745
Input: y = 1, Result x ≈ 4500.6281
Example 2:
a = 2.5, f = 0.94
Input: x = 20, Result y ≈ 1.9134
Input x = 100, Result y ≈ 1.6573
Input y = 2, Result x ≈ 12.1791
Source
Kagan, Julia. “Understanding the Learning Curve: Impact on Efficiency and Costs” Investopedia. May 21, 2026.
https://www.investopedia.com/terms/l/learning-curve.asp Retrieved July 10, 2026
Until next time,
Eddie
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All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
