Saturday, November 05, 2005
Queer Question I
There are normal questions...1. Solve the following differential equations:
(a) x(x + 1)y' = 1
(b) (sec(x))y' = cos(5x)
(c) y' = exp(x−3y)
(d) (1 + y)y' + (1 − 2x)y^2 = 0
There are normal long questions...3. In Biology, the concept of birth rate per capita is important. This is defined as the birth rate (number of babies per unit time) divided by the total population. The death rate per capita is defined similarly. (Why do you think that these numbers are more interesting than the birth and death rates themselves?) The number of bacteria in a certain bacterium culture is 10000 at a certain time. Two and a half hours later there are 11000 of them. Assuming constant birth and death rates per capita, how many bacteria will we have 10 hours after the initial time? How long will it take for the population to reach 20000?
And then,
there are long and queer questions...4. On a certain island the human birth and death rates per capita are constant; and the population doubles in 20 years. However, one day several pirate ships arrive.
All of the island women under the age of 50, tired of being ordered about by their mothers-in-law and ignored by their husbands and boyfriends, decide to elope with the glamorous pirates, taking their children with them. Subsequently the remaining population of the island declines by half over the next ten years. What was the original birth rate per capita on this island? Assume that the men and old women do not die more rapidly as a result of being deprived of the company of the young women and children. What other assumption do you need?
Material taken verbatim from MA1505 Tutorial 8
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Kelvin Lim out
@ |1:36 AM|
