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.