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macleod_callum
03-Dec-06, 21:57
A long shot but I am in need of some help.
Question:
Populations that grow exponentially follow the law:
Nt = N0e^rt
where,
t = time
Nt = inital population
r = growth rate
r = 0.0003 for humans
Assume you start with a male and female of each species at t = 0, calculate:
How long it will take for two humans to create one more.
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Any help appreciated?
Alice in Blunderland
03-Dec-06, 22:10
Would you be requiring diagrams with your answer?!!!:lol:
Should No be the initial population?
wow! that's a tricky one!
if that is what higher maths is all about there is no way i'm doing that! I found int2 hard!
Fraser Macleod
03-Dec-06, 22:22
what does e equal and what is ur unit for time?
macleod_callum
03-Dec-06, 22:25
N0 = inital population.
Uni maths now
macleod_callum
03-Dec-06, 22:28
Little brother,
unit is of time is days.
e is the inverse of a natural log
Colin Manson
03-Dec-06, 22:44
I got 105 but I don't have a calculator here so I had to use Excel, not sure if the formula is correct...
what does e equal and what is ur unit for time?
Hey Pies!
Have you solved it yet?
Antediluvian
03-Dec-06, 23:10
Nt=N0exp(rt)
Nt/N0 = exp(rt)
ln(Nt/No) = ln(exp(rt))
ln(Nt/No)=rt
t=(1/r)*ln(Nt/No)
r=0.0003
N0=2
Nt=3
t=(1/0.0003)*ln(3/2) = 1351.55 time units.. I think somebody said days
105 is a bit optimistic seeing as most pregnancies last approx 270 :)
Bobinovich
03-Dec-06, 23:15
Sheesh - that one flew past me so high over my head I didn't even hear it :eek: !
Congratulations to anyone who even knew where to start...
Colin Manson
03-Dec-06, 23:16
I got 1351.55 before using EXP function but then I changed it to -log.
percy toboggan
03-Dec-06, 23:17
Assume you start with a male and female of each species at t = 0, calculate:
How long it will take for two humans to create one more.
----------
Any help appreciated?
Between two minutes and an hour and a half an hour in my experience, with a subsequent gestation period of about nine months.
Antediluvian
03-Dec-06, 23:21
Yes it is 1351.55, excuse my typing mistake.. think it is more a maths manipulation problem than a realistic population model at lower limits, else this could suggest a a male and female about 4 years old generate a new baby.
Full marks to Antediluvian. I hope tomorrow goes just as well. :)
Yeah, the question is badly posed, but we both figured out what was meant.
I have always been in awe of the great org team no matter what the problem it was tackling.
And good luck tomorrow AnteD.
Antediluvian
03-Dec-06, 23:38
Thanks guys
Tomorrow should be fine, as long as I check my working, am always making careless mistakes as demonstrated..
Biggest one is morning after, Not had much experience of essay questions, am sure it'll be a joy!
macleod_callum
04-Dec-06, 01:19
we originaly got 1831 days (5 years ish) by dividing the by Nzero.
However we finaly got there (four extra students later). 3.7 years.
Cheers
Callum Macleod
Yup, 3.7 years is correct. Antediluvian's solution would get full marks from me.
But you should tell whoever set the question that they shouldn't encourage you to use population statistics to deduce a result for a single couple. He or she does not get full marks. :cool:
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