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A bacterial culture initially contains 3000 bacteria and doubles every half hour. Round to the nearest whole number of bacteria.

Find the size of the bacterial population after 60 minutes.

Answer :

Final answer:

The bacterial population after 60 minutes would be approximately 12,000, as calculated using an exponential growth model formula.

Explanation:

The subject of this question falls under Mathematics, particularly exponential growth models. The situation described is a classic problem of exponential growth, in which a bacteria culture starts with 3000 bacteria and doubles every half hour.

Given this, we can derive an equation to represent the bacteria population at any given time. Define N as the number of bacteria at a given time t (in hours), No as the initial number of bacteria (3000 in this case), and j as a number of generations or doubling times. We can express this situation through the formula:

N = No * 2^j

Since the bacteria doubles every half hour, in 60 minutes or 2 half hours, the number of doubling times j would be 2. Substituting the values No=3000 and j=2 into the formula:

N = 3000 * 2^2

we get N = 12,000. Thus the size of the bacterial population after 60 minutes would be approximately 12,000, rounded to the nearest whole number.

Learn more about Exponential Growth here:

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