Under controlled conditions, the number of a certain type of bacteria doubles every 20 minutes. Suppose the initial number of the bacteria is 1. Which of the following expressions represents the number of 20-minute intervals that it will take for the number of bacteria to equal k?

This choice implies that the number of intervals needed is simply half of (k), which is incorrect because it does not account for the exponential growth nature of the bacteria. Instead, the doubling effect means that the relationship between the intervals and the final count is logarithmic, not linear.

This option suggests that the growth can be represented as a linear proportion of (k) divided by 20. However, this overlooks the fact that the bacteria double every 20 minutes, meaning the growth is exponential rather than linear, making this expression inappropriate.

While the natural logarithm of (k) is involved in solving for intervals, this choice lacks the necessary adjustment to account for the doubling effect of the bacteria. It fails to relate the growth rate to the base of 2, which is crucial since the number of bacteria doubles, not increases linearly.

This expression incorrectly uses the number 20 as a base for the logarithm. The doubling time is relevant to base 2, reflecting how many times (k) can be achieved through continual doubling, making this choice incorrect.