The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours it is observed that 600 bacteria are present. After 10 hours 2000 bacteria are present. What was the initial population of bacteria?
![The number N of bacteria in a culture after t days is modeled by N = 200[1 − 3 (t2+2)2]. Find the rate of change, in bacteria per day, of N with respect to t when the following values are true. (Round your answers to the nearest tenth.) (a) t = 0 bacteria per day (b) t = 1 bacteria per day (c) t = 2 bacteria per day (d) t = 3 bacteria per day (e) t = 4 bacteria per day (f) What can you conclude? After the first day the rate of change of the population is decreasing. The rate of change of the population is always increasing. The rate of change of the population is always decreasing. After the first day the rate of change of the population is increasing. The number of bacteria is only increasing during the first day.](https://www.doubtrix.com/uploads/editor/5517829563SLJlMwWtwH.png)