Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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8. The logistic model is important in the modelling of population dynamics and is represented by
a
N(t) =
1+ ( -1)e-akt
where
N(t) is the population at some time t (days)
No = N(0) is the initial population
a and k are positive constants
• At t = 0 the population is 5
At one week (t = 7) the population is 10
Eventually after a long time the population is 100
ce
(a) Given these three pieces of information provided about the model, find the exact values of No, a
and k.
(b) What is the approximate value of N after two weeks?
(c) Approximately after what time was N = 50?
(d) Sketch the graph of N(t) (labelling all axes,asymptotes and intercepts).
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Transcribed Image Text:8. The logistic model is important in the modelling of population dynamics and is represented by a N(t) = 1+ ( -1)e-akt where N(t) is the population at some time t (days) No = N(0) is the initial population a and k are positive constants • At t = 0 the population is 5 At one week (t = 7) the population is 10 Eventually after a long time the population is 100 ce (a) Given these three pieces of information provided about the model, find the exact values of No, a and k. (b) What is the approximate value of N after two weeks? (c) Approximately after what time was N = 50? (d) Sketch the graph of N(t) (labelling all axes,asymptotes and intercepts).
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