## Friday, January 11, 2008

### Midterm

1. Consider a spherical grad student.*
1a. Assume that information density (D) increases as time elapsed in grad school by the sum of I. an exponential function F including (e)^x where x=1.25 and the half-time of D doubling is 0.6 year and II. a simple sinusoidal function with period=1y. If mental health declines proportionately to 0.2F, calculate the sanity remaining to student N after 5.5 y.

1b. Write an equation for anxiety (A) using chaos equations. Make sure your equation for A includes a random spike every 3 months on average and include a parameter such that anxiety increases with time.
2. Calculate work output:
2a. Determine energy intake E if N takes in approximately 2.5 meals per day and loses weight at the rate of 0.07 kg/ week. Remember to time I as follows: meal 1, 7 a.m.; meal 1.5, 2 p.m.; meal 2.5, 8:30 p.m; and to include a constant rate of energy output during waking hours (17/day).

2b. Work output is proportional to the product of energy input and information density. Express output as an integral function, but do not solve.
3. If sanity is generally described by a shallow hyperbola centered around 'graduation date', explain how any student ever graduates.

*Actual exam question: 'Calculate the capacitance of a human.' And you can imagine how the answer started. (If you can't, see this; first entry under 'Comparisons.')

[PCR, still coming, really, any day now.]