Question

In an actively growing population from a single bacterium, 1,048,576 cells are present after 20th generation. How many cells were there in 5th generation?

Answer 1

Correct Answer: 32

To solve the problem of finding the number of cells in the 5th generation from a single bacterium population where the 20th generation has 1,048,576 cells, we need to understand the concept of exponential growth. In bacterial growth, each generation typically doubles the population. Thus, the number of cells after n generations can be described by the equation: \( N = N_0 \times 2^n \) where \( N \) is the number of cells after n generations, and \( N_0 \) is the initial number of cells. Given the final population (after the 20th generation) is 1,048,576, we know:

\( N = 1, \! 048, \! 576 = 1 \times 2^{20} \)

This confirms that the population size indeed doubled 20 times starting from a single bacterium.

To find the number of cells in the 5th generation, we apply the same formula:

\( N = 1 \times 2^5 = 32 \)

Thus, after the 5th generation, there are 32 cells.