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Do you have what it takes to be a Programmer?
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> 100*1.6^((1/400)*x)-(5*(1/100))*(sum(1.6^((1/400)*i), i = 0 .. x)) = 0.1e9;
fsolve(100*1.6^((1/400)*x)-(5*(1/100))*(sum(1.6^((1/400)*i), i = 0 .. x)) = 0.1e9);
answer:
12229.90861 / 100 hours
this was calculated with maple.
I rewrote the series as:
n(x) = K * a^n - c ( a^(x-1) + a(x-2)...... + 1)
where K is the initial value, a is the rate of growth, and c is the substracted value every hour.
x is the number of hours.