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......
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!