Under controlled conditions, the number of a certain type of bacteria doubles every 20 minutes. Suppose the initial number of the bacteria in the laboratory 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 suggests a linear relationship, implying that the number of intervals corresponds to half of ( k ). However, since the bacteria double every 20 minutes, the relationship is exponential rather than linear, making this expression incorrect.

Similar to choice A, this option also indicates a linear relationship, dividing ( k ) by 20. The actual growth of the bacteria is exponential, and thus the number of intervals cannot be calculated this way. This choice fails to account for the doubling effect every 20 minutes.

This expression incorrectly implies that the number of intervals is simply the natural logarithm of ( k ). While logarithms are involved in the correct calculation, this expression does not consider the base of the exponential growth, which is 2 in this case.

This choice represents the natural logarithm of ( k ) divided by the natural logarithm of 20, which is unrelated to the doubling behavior of the bacteria. It overlooks the fact that the bacteria double every 20 minutes, thus incorrect for determining the required intervals.