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

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

4 hours is equivalent to:
\[
4 \text{ hours} \times 60 \text{ minutes/hour} = 240 \text{ minutes}
\]
\[
\frac{240 \text{ minutes}}{20 \text{ minutes/increment}} = 12 \text{ increments}
\]

Next, we can use the formula given for the population of E. coli:
\[
f(t) = 10 \cdot 2^t
\]
where \( t = 12 \) (the number of 20-minute increments).

Now we can calculate:
\[
f(12) = 10 \cdot 2^{12}
\]

Calculating \( 2^{12} \):
\[
2^{12} = 4096
\]

Then:
\[
f(12) = 10 \cdot 4096 = 40960
\]

Thus, the E. coli population 4 hours after the culture was started is:
\[
\boxed{40,960}
\]