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

Question

, 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

120
120

240
240

160
160

40,960
40,960
Remaini

Answer 1

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: \[ \boxed{40,960} \]