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Constructing an equation

  • Thread starter glid02
  • Start date
54
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Here's the question:
A bacteria culture starts with 820 bacteria and grows at a rate proportional to its size. After 3 hours there will be 2460 bacteria.

(a) Express the population after t hours as a function of t.

I tried y=y'+820, so -y'+y=820
p(t)=1
mu(t)=e^t

I carried this out (multiplying both sides by mu(t) and finding the integral of both sides) and it's not right.

I really don't even know where to start - is finding mu(t) even the right approach?

Thanks a lot.
 

Answers and Replies

cristo
Staff Emeritus
Science Advisor
8,056
72
Your first equation is incorrect.
A bacteria culture starts with 820 bacteria and grows at a rate proportional to its size.
The correct equation for this system would be: [tex]\frac{dy}{dt}=ky[/tex], where k is the constant of proportionality; your equation omitted this!

Try integrating this. The numbers are there as the boundary conditions of the system, to enable you to calculate the constants.
 
54
0
Yep, that was it. Thanks.
 

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