|posted 2 years, 6 months ago||3 replies|
define f(x) as the time needed to reach a solution define x as the time waited in years before presenting the problem to a computer f(x) = 2^(-12x/22) 7.5--10^6+x To find the minimum value of this function,set it's derivative equal to 0. so d/dx(2^(-12x/22) 7.5--10^6+x)=(ln 2)(7.5 * 10^6)(-6/11)(2^(-6x/11)) + 1 set this equal to zero and solve 0=(-2.84 * 10 ^6)(2^(-6x/11)) + 1 x = 39.3 work omitted because of character limit, but it's in my StumbleUpon comment.
I have an excellent proof but unfortunately it was too large to fit in the margins of the comic, or a tweet.
Where Y = total time and X = time waited, you want to minimize Y for X. As seen below in this graph
Our initial work was done by taking the derivative of the first equation with respect to x and evaluating that at 0.