Question

The division of cells creates exponential growth. If 2 cells are present initially and 36 are present after 7 hours, how many cells would there be after 12 hours? Round to the nearest tenth.

Answer 1

To calculate the number of cells after 12 hours, knowing the population doubled from 2 to 36 in 7 hours, we can apply exponential growth, resulting in approximately 1152 cells after 12 hours.

Step-by-step explanation:

The student is asking about exponential growth in cell division, a concept taught in high school mathematics, specifically in algebra and functions. Given that 2 cells are present initially and 36 are present after 7 hours, we can determine that the cell population is doubling every hour. Therefore, we can calculate the number of cells after 12 hours using the formula N = N0 * 2t, where N is the final number of cells, N0 is the initial number of cells, and t is the number of doubling periods (hours, in this case).

To find the number of cells after 12 hours, we can start by calculating the doubling periods between 7 and 12 hours, which is 12 - 7 = 5. Since the number of cells at 7 hours is 36, we apply the doubling for 5 more hours: 36 * 25 = 36 * 32 = 1152 cells. So after 12 hours, there will be approximately 1152 cells.