1. ## Population Models

Hey,

I'm having trouble with a population model question. I have been given the differential equation dN/dt=kN; where t is the time elapsed in hours and k is a constant.

I have also been given some initial conditions; when t=0, N=3000 and when t=3, N=9000

With these values i have been asked to find the value of K

I found the equation to be B(t)=3000e^kt, where K= (1/3)ln(3), does this look right?

Also i have been given the following:
For t > 3 the culture is washed with a solution that is harmful to the bacteria, and the bacteria are killed of 4500 per hour.

Using this i have been asked to find the number of bacteria in the culture for any time where t>3

I am completely stuck for this part of the question!

Any ideas??

Thanks, Function.

2. Dude I have the same problem.

I found the equation to be B(t)=3000e^kt, where K= (1/3)ln(3) too

but the second part is confusing.
I tried to solve again by dN/dt= kN - 4500

but failed to solve......

3. Hi function boy,

Did you say you had a problem with changing gears? I might know someone who can help you out

Thanks, Function.

4. Originally Posted by tdw
Dude I have the same problem.

I found the equation to be B(t)=3000e^kt, where K= (1/3)ln(3) too

but the second part is confusing.
I tried to solve again by dN/dt= kN - 4500

but failed to solve......
$\frac{dN}{kN- 4500}= dt$
Integrating both sides, $\frac{1}{k}ln(kN- 4500)= t+ C$ so $ln(kN- 4500)= kt+ kC$ and then $kN- 4500= e^{kC}e^{kt}= C'e^{kt}$ where $C'= e^{kC}$.

5. Thanks,

I follow what you have done there, but how do i go about solving the variables K and C???? I have tried to use the initial conditions but i dont think that is right, becuase this equation is only for t > 3.

Function

6. Hey function,
I think the intial condition would be t=3 which is N=9000
coz time starts from t=3 so from t=3 on t= 0
haha.... I dunno whether am I right, that the only way I can think about.

7. Hey tdw,
That's what i thought aswell, but that will only give you one variable, and when i tried to do it it just turned into a huge mess . Did you get an answer in the end?
Function