Question

Emily is observing the growth of a bacteria culture in a lab. Initially, there are 100 bacteria in the culture. After 1 hour, the number of bacteria doubles to 200. After 2 hours, it doubles again to 400. What will the number of bacteria be after 12 hours? (1 point) Responses 1,200 bacteria 1,200 bacteria 14,400 bacteria 14,400 bacteria 409,600 bacteria 409,600 bacteria 120,000 bacteria

Answer 1

The bacteria culture doubles every hour. Starting with 100 bacteria, the population can be modeled as:

\[
N(t) = N_0 \times 2^t
\]

where:
- \(N(t)\) is the number of bacteria at time \(t\),
- \(N_0\) is the initial number of bacteria (100 in this case),
- \(t\) is the time in hours.

After 12 hours, we can calculate the number of bacteria as follows:

\[
N(12) = 100 \times 2^{12}
\]

Calculating \(2^{12}\):

\[
2^{12} = 4096
\]

Now, multiply by the initial amount of bacteria:

\[
N(12) = 100 \times 4096 = 409600
\]

So, after 12 hours, the number of bacteria will be **409,600 bacteria**.