Question

The count in a bacteria culture was 100 after 10 minutes and 1100 after 40 minutes. Assuming the count grows exponentially, What was the initial size of the culture? bacteria Find the doubling period. minutes Find the population after 115 minutes. bacteria When will the population reach 10000 . minutes

Answer 1

The initial size of the bacteria culture was 25 and the doubling period was approximately 6.15 minutes. The population after 115 minutes is estimated to be around 10,000, and it will reach this size in approximately 75 minutes.

Step-by-step explanation:

The initial size of the culture can be found using the formula
`\(N_0 = (N)/(2^((t/T)))\)`, where
`\(N_0\)` is the initial size, (N) is the final size, (t) is the time elapsed, and (T) is the doubling period. Substituting the given values, we get
`\(N_0 = (1100)/(2^((40/T))) = 100\)`. Solving for (T), we find
`\(T \approx 6.15\)` minutes.

To find the population after 115 minutes, we can use the formula
`\(N = N_0 * 2^((t/T))\)`. Substituting the values,
`\(N = 25 * 2^((115/6.15)) \approx 10,000\)`.

To determine when the population will reach 10,000, we can rearrange the formula to solve for time (t). Substituting the known values,
`\(10,000 = 25 * 2^((t/6.15))\)`, and solving for (t), we find
`\(t \approx 75\)` minutes.