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This comment is hidden because it contains spoiler information about the solution
Basically, the formula of year n's population is
p0*(1-percent)^n+aug*[(1+percent)^(n-1)+(1+percent)^(n-2)+...+1]
, which is also equal top0*(1-percent)^n+aug*[(1+percent)^n-1]/percent
, thenp0*(1-percent)^n+aug/percent*(1+percent)^n-aug/percent
and finaly(p0+aug/percent)*(1+percent)^n-aug/percent
.By solving
p = (p0+aug/percent)*(1+percent)^n-aug/percent
for n, we can getn = log( (p+aug/percent)/(p0+aug/percent), 1+percent)
.In lechevalier's solution, his
percent
is actually1+percent
and hisr
is-aug/percent
, so his last line becamelog((p-r)/(p0-r), percent)
.