Question

A biologist counts m microbes in a sample. Every day after that, the number of microbes in the sample is multiplied by n. Write expressions for the number of microbes in the sample after one day and after two days. Use these expressions to predict the number of microbes after eight days.

Answer 1

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.