Final answer:
The predicted bacteria population at 6:00 P.M., under the assumption of a constant growth rate, is around 33 million, which assumes a consistent growth of approximately 61.54% over every four hours.
Step-by-step explanation:
This is under the assumption that the bacteria population grows exponentially, which is common in ideal conditions without limitations. Starting with a population of 13 million at 10:00 A.M. that grows to 21 million by 2:00 P.M., this represents a 4-hour span. To predict the population at 6:00 P.M., which is another 4 hours later, we will assume the growth rate is constant.
To find this rate, we take the population at 2:00 P.M. and divide it by the population at 10:00 A.M.: 21 million / 13 million = 1.61538462. This suggests an approximate 61.54% increase in the four hours. Assuming the growth continues at the same rate, we can multiply the 2:00 P.M. population by the growth factor: 21 million * 1.61538462 = 33.9230762 million, which we can round down to 33 million given the options provided. Therefore, the population at 6:00 P.M. would be approximately 33 million.