We are given the following information:

• Initial population $P_0 = 560$
• Doubling time $d = 10$ hours
• Time elapsed $t = 11$ hours

The formula to calculate the population after $t$ hours is:

$P_t = P_0 \cdot 2^{\frac{t}{d}}$

Substituting the known values:

$P_{11} = 560 \cdot 2^{\frac{11}{10}}$

Let's compute $2^{\frac{11}{10}}$ and then multiply by 560 to find the population after 11 hours.The population of bacteria after 11 hours is approximately $1200$ bacteria when rounded to the nearest whole number.

Would you like any additional details on how this was calculated, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. What would the population be after 20 hours?
2. How long will it take for the population to reach 5,000 bacteria?
3. If the doubling time was reduced to 8 hours, how would the population change after 11 hours?
4. How does changing the initial population affect the population after a certain time?
5. Can this formula be used for bacteria that grow at a different rate (e.g., tripling every few hours)?

Tip: Doubling time is crucial in exponential growth problems; always identify it clearly in the formula.