Questions: Wilbur is working in a lab testing bacteria populations. After starting out with a population of 394 bacteria, he observes the change in population and notices population triples every 25 minutes. Find the population after 2 hours. Round to the nearest bacterium.

To find the population of bacteria after 2 hours, given that the population triples every 25 minutes, we can use the formula for exponential growth:

\[ P(t) = P_0 \times r^{(t/T)} \]

where:

• \( P(t) \) is the population at time \( t \),
• \( P_0 \) is the initial population,
• \( r \) is the growth factor (in this case, 3 since the population triples),
• \( t \) is the total time elapsed,
• \( T \) is the time it takes for the population to triple (25 minutes).

Given:

• \( P_0 = 394 \) bacteria,
• \( r = 3 \),
• \( t = 2 \) hours = 120 minutes,
• \( T = 25 \) minutes.

Now, substitute these values into the formula:

\[ P(120) = 394 \times 3^{(120/25)} \]

First, calculate \( 120/25 \):

\[ 120/25 = 4.8 \]

Now, calculate \( 3^{4.8} \):

\[ 3^{4.8} \approx 104.603 \]

Finally, calculate the population:

\[ P(120) = 394 \times 104.603 \approx 41236.782 \]

Rounding to the nearest bacterium, the population after 2 hours is approximately:

\[ \boxed{41237} \] bacteria.