A culture of bacteria has an initial population of 560 bacteria and doubles every 10 hours. Using the formula P, start subscript, t, end subscript, equals, P, start subscript, 0, end subscript, dot, 2, start superscript, start fraction, t, divided by, d, end fraction, end superscriptP 
t
​
 =P 
0
​
 ⋅2 
d
t
​
 
 , where P, start subscript, t, end subscriptP 
t
​
  is the population after t hours, P, start subscript, 0, end subscriptP 
0
​
  is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 11 hours, to the nearest whole number?

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.

A culture of bacteria has an initial population of 560 bacteria and doubles every 10 hours. Using the formula P_t = P_0 ⋅ 2^(t/d), where P_t is the population after t hours, P_0 is the initial population, t is the time in hours, and d is the doubling time, what is the population of bacteria in the culture after 11 hours, to the nearest whole number?

Learn how to calculate the population of bacteria after 11 hours given an initial population of 560 and a doubling time of 10 hours using exponential growth formulas. This problem covers algebraic concepts and exponential growth, suitable for students in Grades 8-10.

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