Constructing a Proportional Growth Equation for Bacterial Population

[glid02]

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.

 

[cristo]

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: $$\frac{dy}{dt}=ky$$, 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.

 

[glid02]

Yep, that was it. Thanks.