The problem you've provided describes exponential growth. The population of bacteria doubles every hour, starting with 100 bacteria. To solve for the population after 5 hours, we can use the formula for exponential growth:

$P(t) = P_0 \times 2^t$

Where:

• $P(t)$ is the population at time $t$ (in hours),
• $P_0$ is the initial population,
• $t$ is the time in hours,
• The base 2 represents the doubling.

Given:

• $P_0 = 100$ (initial population),
• $t = 5$ hours.

Substituting these values into the formula:

$P(5) = 100 \times 2^5 = 100 \times 32 = 3200$

Answer:

After 5 hours, there will be 3,200 bacteria.

Would you like further details or clarifications? Here are 5 questions related to exponential growth:

1. How would the population change if it tripled every hour instead of doubling?
2. Can you derive the time it would take for the population to reach 10,000 bacteria?
3. What is the general form of the exponential growth equation?
4. How does the growth rate affect the population size over a long period?
5. What happens to the population as time approaches infinity?

Tip: Exponential growth increases rapidly, and small changes in growth rates can lead to large differences over time.