A culture of bacteria has an initial population of 6100 bacteria and doubles every 5 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 12 hours, to the nearest whole number?

We are given the formula for population growth as:

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

Where:
- \( P_t \) is the population after \( t \) hours,
- \( P_0 = 6100 \) is the initial population,
- \( t = 12 \) hours is the time we are interested in,
- \( d = 5 \) hours is the doubling time.

Now, we will substitute the given values into the formula to find the population after 12 hours:

\[
P_{12} = 6100 \cdot 2^{\frac{12}{5}}
\]

First, calculate \( \frac{12}{5} \):

\[
\frac{12}{5} = 2.4
\]

Now, calculate \( 2^{2.4} \), then multiply the result by 6100 to get the population after 12 hours.

Let me compute that for you.The population of the bacteria after 12 hours is approximately 32,196 (rounded to the nearest whole number).

Would you like further details or have any other questions?

Here are 5 related questions you can explore:
1. What would the population be after 24 hours?
2. How long would it take for the population to reach 100,000 bacteria?
3. If the doubling time changes to 6 hours, what would the population be after 12 hours?
4. How would the population change if the initial population were 10,000 instead of 6,100?
5. What is the formula for continuous population growth if the rate is not constant?

**Tip:** Doubling time refers to the period it takes for a quantity to multiply by two, often used in exponential growth models.

A culture of bacteria has an initial population of 6100 bacteria and doubles every 5 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 12 hours, to the nearest whole number?

Find the population of bacteria after 12 hours, starting with an initial population of 6100 that doubles every 5 hours. Learn how to use the exponential growth formula to calculate the population after a given time period. Suitable for students in Grades 9-11.

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