This question refers to Budish$$s back$-$of$-$the$-$envelope calculation of how big the trans$-$ action fee needs to be in order to fend off a double$-$spending attack.

Suppose the attacker needs to rent K $\backslash$times N $($instead of $1\mathrm{.}05\backslash$times N$)$ computers, where K $>1.$ Express the necessary fee as a function of K$.$ What is the derivative of the necessary fee with respect to K$?$ Does the sign of the derivative make sense to you? Why or why not?