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Above gave the calculus solution in algebra and also values from discrete arithmetic with (10)(365) steps per year. For the arithmetic for the calculus solutio
by graycat 2y ago
Above gave the calculus solution in
algebra and also values from discrete
arithmetic with (10)(365) steps per year.
For the arithmetic for the calculus
solution, in Rexx,
y.0 = ( 1 / 100 )
b = 1
k = ( 1 / 2000 )
Do t = 1 To 5
t1 = t * (10 * 365 )
e1 = RxCalcExp( b * k * t1, 16 )
y.t = ( y.0 * e1 ) / ( y.0 * ( e1 - 1 ) + b )
Say Format(t,9) Format(100*y.t,6,2) || '%'
End
Table below has the values from both the
calculus and the discrete versions:
==== Growth ====
Customer Fraction
Year Calculus Discrete
1 5.90% 5.89%
2 27.99% 27.97%
3 70.68% 70.66%
4 93.73% 93.73%
5 98.93% 98.93%
Lesson: Sometimes in growth problems with
a calculus solution, a discrete version
can give close results.