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Let's solve the problem:

**Given:**
- The bacteria colony doubles every 6 hours.
- We need to find out how many hours it will take for the bacteria to be 5 times the original amount.

This is a typical exponential growth problem. We can use the following formula for exponential growth:

\[
N(t) = N_0 \cdot 2^{\frac{t}{T}}
\]

Where:
- \(N(t)\) is the number of bacteria at time \(t\),
- \(N_0\) is the initial number of bacteria,
- \(T\) is the doubling time (6 hours in this case),
- \(t\) is the time elapsed in hours.

We are asked to find \(t\) when the bacteria is 5 times the original amount, i.e., \(N(t) = 5N_0\). Substituting into the equation:

\[
5N_0 = N_0 \cdot 2^{\frac{t}{6}}
\]

Dividing both sides by \(N_0\) (since \(N_0 \neq 0\)):

\[
5 = 2^{\frac{t}{6}}
\]

Now, take the logarithm (base 2) of both sides:

\[
\log_2(5) = \frac{t}{6}
\]

Solving for \(t\):

\[
t = 6 \cdot \log_2(5)
\]

We can convert the base 2 logarithm into base 10 (or natural logarithm):

\[
t = 6 \cdot \frac{\log(5)}{\log(2)}
\]

Let me calculate this for you.The correct time it will take for the bacteria to become 5 times the original amount is approximately **13.932 hours**, rounded to three decimal places.

It looks like the answer you provided, **13.931**, was very close but slightly off due to rounding. 

Would you like further details or have any questions about the calculation?

Here are some related questions:
1. What is the general formula for exponential growth and decay?
2. How can we calculate the time for different multiplication factors (e.g., 3 times, 10 times)?
3. How does changing the doubling time affect the growth?
4. What other natural processes follow exponential growth patterns?
5. How would the calculation change if the doubling time were 8 hours instead?

**Tip:** Always check for rounding errors when precision is required to a specific decimal point!

If the size of a bacteria colony doubles in 6 hours, how many hours will it take for the number of bacteria to be 5 times the original amount? Round to 3 decimal places.

Learn how to calculate the time it takes for a bacteria colony to grow 5 times its original size when the colony doubles every 6 hours. This problem involves exponential growth and logarithmic calculations. Suitable for high school students in Grades 10-12.

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