Answer:
The instantaneous growth rate of the bacteria will be 200 cells per hour after 3 hours.
Explanation:
There are four phases of bacterial growth represented by a bacterial growth curve, and they are; the lag phase, the log/exponential phase, the stationary phase, and the decline phase.
Under favorable conditions of nutrients, temperature, pH, oxygen and space, bacterial cells grow at a geometric or exponential rate this is the log phase, this means that the population doubles after a regular interval of time. In order to determine the time to attain a growth rate of 200 cells per hour, we have to start from the growth rate at 1 hour from the start and work upwards, and this is calculated thus;
it was given that after 2 hours, the population increased from 1800 to 1900, meaning that after 2 hours the growth rate was 100 cells per hour
∴ 0 to 2 hours = 100 cells/hour
2 hours = 100 cells/hour
∴ 1 hour = 100/2 = 50 cells/hour.
After the first hour, the growth rate was 50 cells/hour. Remembering that exponential growth is doubling of a population at an equal time interval (1 hour)
1 hour = 50 cells/hour
2 hours = 50 + 50 = 100 cells/hour
3 hours = 100 + 100 = 200 cells/ hour
4 hours = 200 + 200 = 400 cells/hour
This continues until the bacteria reaches the stationary phase of the growth curve then begins to decline.
so from the calculation above, at 3 hours the growth rate is 200 cells per hour.
I suggest you read up bacterial growth phases for better understanding.
