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 be the number of bacteria after 12 hours?

Question

1)14,400
2)1,200
3)409,600
4)120,000

Answer 1

The bacteria culture doubles every hour. Starting with 100 bacteria, we can calculate the number of bacteria after \( n \) hours using the formula:

\[ \text{Number of bacteria} = \text{Initial amount} \times 2^n \]

Here, the initial amount is 100, and \( n \) is the number of hours (in this case, 12).

So we compute:

\[ \text{Number of bacteria after 12 hours} = 100 \times 2^{12} \]

Now, calculate \( 2^{12} \):

\[ 2^{12} = 4096 \]

Then we can find the total number of bacteria:

\[ 100 \times 4096 = 409600 \]

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

So the answer is 3) 409,600.