Question 122541
This looks like exponential growth.
The formula for exponential growth is
{{{f(t)=k*e^((alpha) t)}}}
We just need to determine {{{k}}} and {{{alpha}}}
{{{f(1)=k*e^((alpha))=5}}}
{{{f(2)=k*e^(2(alpha))=10}}}
{{{e^(2(alpha))/e^(alpha)=10/5}}}
{{{e^(alpha)=2}}}
{{{(alpha)=ln(2)}}}
{{{(alpha)=0.693}}}

{{{f(1)=k*e^((alpha))=5}}}
{{{k*e^(0.693)=5}}}
{{{2k=5}}}
{{{k=2.5}}}
{{{f(t)=2.5*e^(0.693t)}}}
So, what is t so that f(t)>1000000
{{{2.5*e^(0.693t)>1000000}}}
{{{e^(0.693t)>400000}}}
{{{0.693t>ln(400000)}}}
{{{0.693t>12.89922}}}
{{{t>18.61}}}
The first time would be the 19th correct question. 
For 19 correct answers, you would win
{{{f(19)=2.5*e^(0.693(19))}}}
{{{f(19)=2.5*e^(13.167)}}}
{{{f(19)=1307059.78}}}
The payout would be $1.307,059.78.