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Bacteria Growth Problem.

by QuantumTheory
Tags: bacteria, growth
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QuantumTheory
#1
May11-05, 12:22 AM
P: 224
My friend had to do this problem in Calculus BC. I'm no good at calculus, but I decided it was be fun for someone to figure it out for me.

A bacteria culture starts with 500 bacteria and grows at a rate proportional to its size. After 3 hours there are 8000 bacteria.
(a) Find an expression for the number of bacteria after t hours.
(b) Find the number of bacteria after 4 hours.
(c) Find the rate of growth after 4 hours.
(d) When will the population reach 30,000?

I think it involves differential equations.
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Corneo
#2
May11-05, 01:28 AM
P: 321
Quote Quote by QuantumTheory
but I decided it was be fun for someone to figure it out for me.


Start with [tex]y=Ae^{kt}[/tex]
Jayboy
#3
May11-05, 05:31 AM
P: 21
Yeah that amused me too .I'd probably start a little earlier:

Growth proportional to size implies.....

[tex]\frac{dy}{dt}=ky[/tex]

with the intial condition [tex]y(0)=500[/tex] and the time t = 3 (in hours!) condition [tex]y(3)=8000[/tex].

Your mission, should you choose to accept it, is to find the general solution to the DE above, and the values of k and the constant of integration A.

That's the model, the rest should be ok?


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