## Problem of the Day #86: AMT Adrenaline
*June 13, 2011*

*Posted by Seungln in : potd , trackback*

As the end of the school year approaches, Saketh decides to start on all of the AMT homeworks that were due during 4th quarter. Saketh figures that the workload would keep him up all night.. The thought of that pumps adrenaline through his body.

The amount of adrenaline pumped inside Saketh can be represented by this function:

$$f(t) = \frac{1}{(9-t)^4}$$

When $t$ is the number of hours before 7:00, the time Saketh has to leave the house in order to arrive exactly at 8:30, when school starts.

If he requires 200 units of work (which will now be referred to as ‘psi’) to finish an AMT homework and he gathers up $$8000 \cdot \Sigma_{p=x}^{7} f(p)$$ psi every hour at the hour, what is the largest *integer* $x$ such that Saketh can start on his AMT homework at $x$ a.m. without having to do any of it at school?

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