exponential growth problem

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• Jan 22nd 2010, 12:41 PM
bhuang
exponential growth problem
I have totally forgotten how to do these questions, so I would really like to check my work...

A bacteria culture starts with 3000 bacteria and grows to a population of 12000 after 3 hours.
a) Find the doubling period.
b) Determine the number of bacteria after 8 hours.

what i did was...
a) 12000 = 3000r^3
and got r=1.59

b) A=3000(1.59)^8
=122545.7

Is that right?
• Jan 22nd 2010, 12:49 PM
e^(i*pi)
Quote:

Originally Posted by bhuang
I have totally forgotten how to do these questions, so I would really like to check my work...

A bacteria culture starts with 3000 bacteria and grows to a population of 12000 after 3 hours.
a) Find the doubling period.
b) Determine the number of bacteria after 8 hours.

what i did was...
a) 12000 = 3000r^3
and got r=1.59

b) A=3000(1.59)^8
=122545.7

Is that right?

The working is good, didn't check your arithmetic (Cool)
• Jan 23rd 2010, 04:14 AM
HallsofIvy
Quote:

Originally Posted by bhuang
I have totally forgotten how to do these questions, so I would really like to check my work...

A bacteria culture starts with 3000 bacteria and grows to a population of 12000 after 3 hours.
a) Find the doubling period.
b) Determine the number of bacteria after 8 hours.

what i did was...
a) 12000 = 3000r^3
and got r=1.59

That is r, but does not answer the question. Yes, 12000/3000= 4. 4 is 2 doubled and 2 is one doubled: the population has doubled twice in 3 hours. How long is each doubling period then?

Quote:

b) A=3000(1.59)^8
=122545.7

Is that right?
(b) is approximately correct but notice that $r^3= 4$ so r is actually $4^{\frac{1}{3}}$ so the exact answer is 3000(4^{\frac{8}{3}}[/tex] which is (again approximately but, I think, more accurate) 120952.

Once you have the correct answer to (a) you could also do that as $3000(2^{\frac{8}{T}}$ where "T" is the doubling time.