Maths

[macleod_callum]

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.
----------

Any help appreciated?

[Alice in Blunderland]

Would you be requiring diagrams with your answer?!!!:lol:

[Tristan]

Should No be the initial population?

[Big G]

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]

what does e equal and what is ur unit for time?

[macleod_callum]

N0 = inital population.

Uni maths now

[macleod_callum]

Little brother,

unit is of time is days.

e is the inverse of a natural log

[Colin Manson]

I got 105 but I don't have a calculator here so I had to use Excel, not sure if the formula is correct...

[gollach]

what does e equal and what is ur unit for time?

Hey Pies!
Have you solved it yet?

[Antediluvian]

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]

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]

I got 1351.55 before using EXP function but then I changed it to -log.

[percy toboggan]

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]

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.

[DrSzin]

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.

[canuck]

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]

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]

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

[DrSzin]

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: