A culture of bacteria has an initial population of 8600 bacteria and doubles every 6 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 7 hours, to the nearest whole number?

The given formula for bacterial growth is:

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

Where:
- \( P_t \) is the population after \( t \) hours,
- \( P_0 = 8600 \) is the initial population,
- \( t = 7 \) hours is the time we want to calculate the population for,
- \( d = 6 \) hours is the doubling time.

We can now substitute these values into the formula:

\[
P_7 = 8600 \cdot 2^{\frac{7}{6}}
\]

Now, let's calculate it step-by-step:

1. Calculate \( \frac{7}{6} \).
2. Raise 2 to that power.
3. Multiply the result by 8600.

I'll compute this for you.The population of bacteria after 7 hours is approximately 19,306.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. What will the population be after 12 hours?
2. How long will it take for the population to reach 50,000?
3. What is the population after 1 day (24 hours)?
4. How does changing the doubling time affect the population after 7 hours?
5. How would the population change if it started at 10,000 bacteria instead?

**Tip**: Exponential growth can lead to very rapid increases in population. Always pay attention to the doubling time to understand the growth rate better.

A culture of bacteria has an initial population of 8600 bacteria and doubles every 6 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 7 hours, to the nearest whole number?

Discover how to calculate the population of a bacteria culture with an initial population of 8600 that doubles every 6 hours. Using the exponential growth formula P_t = P_0 ⋅ 2^(t/d), learn how to determine the population after 7 hours. This example highlights exponential growth and algebraic concepts for students in Grades 9-12.

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