Questions: A bacteria culture initially contains 2000 bacteria and doubles every half hour. Find the size of the bacterial population after 20 minutes. Find the size of the bacterial population after 7 hours.

Solution Steps

To find out how many times the population has doubled, we divide the future time (0.333) by the doubling interval (0.5). \[N = \frac{0.333}{0.5} = 0.667\]

Using the formula \(P = P0 \times 2^N\), where \(P0\) is the initial population size, and \(N\) is the number of doubling intervals, we find the future population size. Given \(P0 = 2000\) and \(N = 0.667\), \[P = 2000 \times 2^{0.667} = 3174.8\]

Final Answer: The size of the bacterial population after 0.333 units of time will be approximately 3174.8.