## Start Slow, Grow Exponentially

The hardest part about doing anything new is getting started. We are all familiar with the usual big start and quick quit. An alternative is to start off very slow when the going is harder and take the larger steps after becoming stronger. A spreadsheet can be calculated electronically (first example), or alternatively, self-reliantly by hand. This also works to learn (or teach) patience.

Choose First Step: L1
Choose Last Step: LL
Choose # of Steps: N
R = LL – L1
i = increment 1 to N
Y = (i – 1) / (N – 1)
Time(i) = (((10 ^ (log10(101) * Y)) – 1) * R * .01) + L1

 L1 LL N R Log10(101) 0.25 30 10 29.75 2.0043
 i y Time 1 0.000 0.25 2 0.111 0.45 3 0.222 0.78 4 0.333 1.34 5 0.444 2.27 6 0.556 3.82 7 0.667 6.40 8 0.778 10.73 9 0.889 17.95 10 1 30.00

A worksheet to calculate manually without electronics:

 L1 LL N R log10(101) 0.25 30 10 29.75 2.0043
 a b c d e f g h i i-1 b/(N-1) c*log10(101) 10^d e-1 f*R*.01 g+L1 1 0 0 0 1 0 0 0.25 2 1 0.11 0.22 1.67 0.67 0.20 0.45 3 2 0.22 0.45 2.79 1.79 0.53 0.78 4 3 0.33 0.67 4.66 3.66 1.09 1.34 5 4 0.44 0.89 7.78 6.78 2.02 2.27 6 5 0.56 1.11 12.99 11.99 3.57 3.82 7 6 0.67 1.34 21.69 20.69 6.15 6.40 8 7 0.78 1.56 36.22 35.22 10.48 10.73 9 8 0.89 1.78 60.48 59.48 17.70 17.95 10 9 1.00 2.00 101.00 100.00 29.75 30.00