This program is Copyright © 1978 by HewlettPackard and is used here by permission. This program was originally published in "HP33E Student Engineering Applications".
This program is supplied without representation or warranty of any kind. HewlettPackard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.
Many growth or decay phenomena encountered in science and engineering obey an exponential law of the general form:
X_{t} = X_{ss}  (X_{ss}  X_{0})e^{t/K}
where:
X_{t} = Value at any time, t, (i.e., the instantaneous value)
X_{ss} = Steady state value (i.e., at t = infinity)
X_{0} = Initial Value (i.e., at t = 0)
t = Elapsed time (time after t = 0)
K= Exponential timeconstant for specific phenomena
This program provides interchangeable solutions for any one of the four variables X_{t}, X_{ss}, X_{0}, or t provided three variables and K are known.
Step 
Instructions 
Input Data/Units 
Keys 
Output Data/Units 
1 
Enter program 

2 
Store time constant 
K 
STO 4 

3 
Store variables: 




Initial value  X_{0} 
STO 0 


Instantaneous value  X_{t} 
STO 1 


Steady state value  X_{ss} 
STO 2 


Elapsed time  t 
STO 3 


(Store any 3 of the 4 variables) 



4 
To Calculate: 




X_{0}, Initial value 

GSB 21 
X_{0} 

X_{t}, Instantaneous value 

GSB 01 
X_{t} 

X_{ss}, Steady state value 

GSB 09 
X_{ss} 

t, Elapsed time 

GSB 29 
t 
5 
For a new case go to step 2. 

Given a 5uF capacitor in series with a 1 megohm resistor. 1.5 seconds after the circuit is completed 125 volts are measured across R. To what voltage was the capacitor originally charged?
Note: K = the RC timeconstant, and the voltage at t = infinity is zero.
Keystrokes Display 5 EEX CHS 6 ENTER EEX 6 x STO 4 125 STO 1 0 STO 2 1.5 STO 3 GSB 21 168.7324 (volts)
A cobalt 60 source (half life = 5.26 years) had an activity of 3.54 curies when purchased 8.5 years ago. What is its present activity?
Note: Activity at t = infinity will be zero, K = half life/ln 2.
Keystrokes Display 5.26 ENTER 2 f LN ÷ STO 4 3.54 STO 0 0 STO 2 8.5 STO 3 GSB 01 1.1549 (curies)
LINE CODE KEYS 00 f CLEAR PRGM 01 24 0 RCL 0 02 24 2 RCL 2 03 41  04 12 40 GSB 40 05 71 ÷ 06 24 2 RCL 2 07 51 + 08 13 00 GTO 00 09 12 40 GSB 40 10 31 ENTER 11 31 ENTER 12 24 1 RCL 1 13 61 x 14 24 0 RCL 0 15 41  16 21 x<>y 17 1 1 18 41  19 71 ÷ 20 13 00 GTO 00 21 12 40 GSB 40 22 24 1 RCL 1 23 24 2 RCL 2 24 41  25 61 x 26 24 2 RCL 2 27 51 + 28 13 00 GTO 00 29 24 0 RCL 0 30 24 2 RCL 2 31 41  32 24 1 RCL 1 33 24 2 RCL 2 34 41  35 71 ÷ 36 14 1 f LN 37 24 4 RCL 4 38 61 x 39 13 00 GTO 00 40 24 3 RCL 3 41 24 4 RCL 4 42 71 ÷ 43 15 1 g e^{x} 44 15 12 g RTN
R0 X_{0} R1 X_{t} R2 X_{ss} R3 t R4 K
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