A bacteria culture starts with 2,000 bacteria and doubles in size every 4 hours. Find an exponential model for the size of the culture as a function of time $t$ in hour $f(t)=2000 \cdot 2^{\left(\frac{t}{4}\right)}$

Use the model to predict how many bacteria there will be after 2 days. (Round your answer to the nearest hundred thousand.) bacteria

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Step 1 ：The problem is asking for an exponential model for the size of the bacteria culture as a function of time. The initial size of the culture is 2000 bacteria and it doubles every 4 hours. This can be represented by the function \(f(t)=2000 \cdot 2^{\left(\frac{t}{4}\right)}\) where \(t\) is the time in hours.

Step 2 ：The second part of the question asks to predict the size of the bacteria culture after 2 days. We can substitute \(t\) with the number of hours in 2 days (48 hours) into the function to get the predicted size.

Step 3 ：Substitute \(t = 48\) into the function to get the predicted size.

Step 4 ：The predicted size of the bacteria culture after 2 days is approximately \(\boxed{8,192,000}\) bacteria.