Question

A biologist grows a culture of bacteria as part of an experiment. At the start of the experiment, there are 75 bacteria in the culture. The biologist observes that the population of bacteria doubles every 18 minutes. Which of the following equations best models the number, n, of bacteria in hours after the start of the experiment?

Answer 1

The equation that models the exponential growth of bacteria doubling every 18 minutes, starting with 75 bacteria, is n(t) = 75 × 2^(t/0.3), where t is the time in hours.

Step-by-step explanation:

The student is asking for the equation that models the number of bacteria in a culture that doubles every 18 minutes. This situation is an example of exponential growth. Because there are 75 bacteria initially and the doubling occurs every 18 minutes, we can model this growth with the function n(t) = 75 × 2^(t/0.3), where t is the time in hours (since 18 minutes is 0.3 of an hour) and n(t) is the number of bacteria at time t.