The population of Alaska from 1900 to 2000 can be modeled by the following logistic equation y(t) = 895598/(1 + 71.57e^(-0.0516t)), where y is the population and t is years after 1900, with t = 0 corresponding to 1900, t = 10 corresponds to 1910, t = 20 corresponds to 1920, etc. Which of the following is the rate of change of the population in 1930? (The units are people per year.)A. rate = 2673B. rate = 4127C. rate = 3721
logistic equation
2011-10-14 9:57 am
回答 (2)
2011-10-14 3:37 pm
✔ 最佳答案
(1 + ae^bt)y = k, where a = 71.57, b = - 0.0516 and k = 895598By Product Rule, (1 + ae^bt)(dy/dt)+ y(abe^bt) = 0
dy/dt = - y(abe^bt)/(1 + ae^bt) = - kabe^bt/(1 + ae^bt)^2
Now t = 30
so rate of change = y' = - (895598)(71.57)(- 0.0516)e^(- 0.0516 x 30)/[1 + 71.57e^(-0.0516 x 30)]^2 = 703405.83/263.12 = 2673.3. So answer is A.
2011-10-14 6:55 pm
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