Pseudomonas sp. is a bacteria that can divide every 30 minutes under ideal conditions. If there are 100 bacteria under ideal conditions, how many will be present in 2 hours?

Steps to Solve

1. Calculate the number of 30-minute intervals in 2 hours

Since there are 60 minutes in an hour, 2 hours contain $2 \times 60 = 120$ minutes.

The bacteria divide every 30 minutes, therefore the number of intervals is $120 / 30 = 4$.

2. Calculate the population after each division

The initial population is 100. After each 30-minute interval, the population doubles.

After the first 30 minutes: $100 \times 2 = 200$

After the second 30 minutes: $200 \times 2 = 400$

After the third 30 minutes: $400 \times 2 = 800$

After the fourth 30 minutes: $800 \times 2 = 1600$

3. Express the calculation as an exponential growth formula

The general formula for exponential growth is $P(t) = P_0 \times 2^n$, where:

$P(t)$ is the population after time $t$

$P_0$ is the initial population

$n$ is the number of division intervals

In this case, $P_0 = 100$ and $n = 4$.

Therefore, $P(2) = 100 \times 2^4 = 100 \times 16 = 1600$.