A bacterial culture in a bioreactor has an initial population of 5 10^6 cells. Over the next few days, the population size is observed to remain exactly constant at 5 10^6 cells. If the per-capita birth rate of this population is 0.12 per day, what is the per-capita death rate per day?

Step-by-step solution

For a population to remain constant in size over time, the intrinsic rate of natural increase ( r ) must be zero. The intrinsic rate of natural increase is given by the difference between the per-capita birth rate ( b ) and the per-capita death rate ( d ): r = b - d . Given that the population size is constant, r = 0 . Therefore, 0 = b - d d = b . Since the per-capita birth rate ( b ) is given as 0.12 per day, the per-capita death rate ( d ) must also be 0.12 per day. Multiplying the rate by the population size inc