Question

In a lab experiment, 30 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 6 hours. How many bacteria would there be after 19 hours, to the nearest whole number?

Answer 1

To determine the number of bacteria after 19 hours, we can use the concept of exponential growth. The bacteria double every 6 hours.

First, we determine how many 6-hour intervals are in 19 hours:

\[
\text{Number of intervals} = \frac{19 \text{ hours}}{6 \text{ hours/interval}} \approx 3.1667
\]

This means that there are 3 complete 6-hour intervals in 19 hours.

Next, for each interval, the number of bacteria doubles. Therefore, we can calculate the bacteria population after 3 intervals as follows:

1. Start with 30 bacteria.
2. After 1 interval (6 hours): \(30 \times 2 = 60\)
3. After 2 intervals (12 hours): \(60 \times 2 = 120\)
4. After 3 intervals (18 hours): \(120 \times 2 = 240\)

Now, after 18 hours, there are 240 bacteria.

Since there is an additional 1 hour remaining until the 19-hour mark, we must calculate what happens during this additional hour. Because the bacteria do not double again until the next full 6-hour period, we still have 240 bacteria after 19 hours.

Thus, the total number of bacteria after 19 hours, to the nearest whole number, is:

\[
\boxed{240}
\]