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The population of Aedesmosquitoes which carry the Dengue virus can be modeled by a differentialequation which describes the rate of growth of the population. The populationgrowth rate
dP/dt is given bydP/dt=rP(1-P/k), where r ispositive constant and k is the carrying capacity.
1) When the population is small, the relativegrowth rate is almost constant. What do you understand by the term relativegrowth rate?
2) (a) Show that if the population does not exceedits carrying capacity, then the population is increasing.
b) Show that if the population exceeds itscarrying capacity, then the population is decreasing.
3) (a) suppose that the initial population is P₀. Discuss, by considering the sign ofdP/dt, therelationship between P and k if P₀ is less than k and if P₀ is greater than k.
(b) Determine the values of P for constant growth,increasing growth and declining growth.
4) Determine the maximum value of dP/dtandinterpret the meaning of this maximum value.
5) Express P in terms of r, k and t. Usingdifferent initial population sizes P₀, r and k, plot, on the same axes, a few graphs to show the behavior ofP versus t.
6) The population sizes of the mosquitoes in acertain area at different times, in days, are given in the table below.
Time (days) Number of mosquitoes
0 40
35 77
63 125
91 196
105 240
126 316
140 371
182 534
203 603
224 658
245 701
252 712
322 776
371 791
392 794
406 796
441 798
504 799
539 800
567 800
It is interesting to determine the carryingcapacity and the growth rate based on the above data to control the populationof Aedes mosquitoes. Using different values of P and t, plot ΔP/Δtagainst P andhence obtain the approximate values for r and k.这是我们stpmsecond sem 的题目，我后无头绪，希望你们可以帮忙。
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发表于 25-1-2013 11:10 PM
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