Question

In a lab setting, E. coli bacteria can double every 20 minutes. An E. coli culture that starts with 10 E. coli can be modeled by f(t)=10⋅2t
, where t is the number of 20-minute increments after the culture was started. What is the E. coli population 4 hours after the culture was started?(1 point)
Responses

240
240

120
120

40,960
40,960

160

Answer 1

To find the E. coli population 4 hours after the culture was started, we first need to convert the time from hours to 20-minute increments.

There are 60 minutes in an hour, so:
- In 4 hours, there are \(4 \times 60 = 240\) minutes.
- Since each increment is 20 minutes, we divide the total minutes by 20:
\[
\frac{240}{20} = 12.
\]
So, \(t = 12\) increments of 20 minutes.

Now, we can use the function \(f(t) = 10 \cdot 2^t\) to find the population:
\[
f(12) = 10 \cdot 2^{12}.
\]

Next, we calculate \(2^{12}\):
\[
2^{12} = 4096.
\]

Now, we multiply by 10:
\[
f(12) = 10 \cdot 4096 = 40960.
\]

Thus, the E. coli population 4 hours after the culture was started is \(40,960\).

Therefore, the correct response is:
**40,960**.