Question

Initially, 40 bacteria are placed in a Petri dish. It is observed that the bacteria triple in population every 11 hours.

The scenario can be modeled by the function f(x) = 40 * 3^(x/11), where f(x) represents the population of bacteria x hours after they are placed in the Petri dish. (True/False)
After 4 hours, there are approximately 60 bacteria. (True/False)

Answer 1

Using the exponential growth function provided, after substituting 4 for x, it is determined that the population of bacteria after 4 hours is approximately 60, making the statement True.

Step-by-step explanation:

The question deals with the exponential growth of a bacterial population in a Petri dish, modeled by a mathematical function. We are given the function f(x) = 40 · 3^(x/11), where f(x) represents the bacterial population x hours after the initial placement. This model implies that the population triples every 11 hours.

To determine the accuracy of the statement 'After 4 hours, there are approximately 60 bacteria,' we must substitute 4 for x in the function to calculate the expected population size:

f(4) = 40 · 3^(4/11) ≈ 40 · 1.515 = 60.6.

Therefore, the statement is True, as the calculated result of approximately 60 is very close to the actual number of bacteria after 4 hours according to the model.