im stuck on ii(i) find k3) A culture of bacteria is growing at a rate proportional to the number,

, of bacteria present, so that:

where is the time elapsed in hours and is a constant.

Initially, the culture contains 3000 bacteria,

and after three hours, it contains 9000 bacteria.

(i) Find k.

Thereafter (that is, for t > 3), the culture is washed with a solution

which is harmful to the bacteria, and the bacteria are killed off

at a constant rate of 4500 per hour.

(ii) Find the number of bacteria in the culture for any time t > 3.

(iii) After how much washing time (hours/minutes) do the bacteria die out?

I got

Which gives: ...............................

ii) find the population after 3 hrs (i.e. t>3)

Ok. so first I thought it was

then i thought it this:

Now im thinking

yeh so any tips...is it the last one?