# Calculations Based On First-order Linear Differential Equations - HP -22S Owner's Manual

Scientific calculator.

Calculations Based on First-Order Linear
Differential Equations
The following equation can be used for a wide variety of calculations
involving exponential growth and decay:
Y=F+(I-F)xEXP(KXT)
where
K
=
F=
the growth or decay constant.
[ =
T=
¥=
the final value. F occurs at T
=
+00
for negative val-
ues of
K,
and at
T
=
-
00
for positive values of
K.
the value at T = O.
elapsed time.
the value at time
T.
Example: An RC Circuit.
Part 1.
For the circuit shown below, calcu-
late the voltage across the capacitor 5 seconds after the switch is
closed. At
T
=
0, the voltage across the capacitor is O.
(K
=
-1
+
(R x
C".
R
=
1MQ
Keys:
Display:
'EVAL
I
F?value
6
'INPUT
I
I
?value
o
'INPUT
I
K?value
.1II60
10
.1II-6
G
'1Ix
I
ElJ
'INPUT
I
K=-0.1000
T?value
C
=
10ILF
T
Description:
Prompts for F.
Stores F (voltage at T
=
00),
prompts for [.
Stores [ (the voltage
before the switch is
closed), prompts for K.
Calculates and stores
K,
prompts for
T.
7: The Equation Library
107  