Final answer:
The number of microbes after one and two days can be expressed as mn and mn^2 respectively. To predict the number after eight days, we use m * n^8, demonstrating exponential growth.
Step-by-step explanation:
If a biologist counts m microbes in a sample and every day after that the number of microbes is multiplied by n, then:
- The number of microbes after one day would be mn.
- The number of microbes after two days would be m * n * n or m * n^2.
To predict the number of microbes after eight days, we'd use the expression m * n^8. This is based on the principle of exponential growth, where the growth rate is continuously increasing, and the population size increases at a greater rate over time.
This pattern of growth is represented by a J-shaped curve when the population size N is plotted over time, showing the rapid increase in population size as time progresses.