Question
a colony of 10,710 bacteria doubles in size every 129 minutes. what will be 516 minutes from now
Answers
GPT-4o mini
To find out how many bacteria there will be after 516 minutes, we first need to determine how many doubling periods occur in that time.
1. **Calculate the number of doubling periods:**
\[
\text{Number of doubling periods} = \frac{\text{Total time}}{\text{Time per doubling}} = \frac{516 \text{ minutes}}{129 \text{ minutes}} \approx 4
\]
2. **Determine the number of bacteria after 4 doublings:**
Since the colony doubles in size with each period, we can use the formula:
\[
\text{Final population} = \text{Initial population} \times 2^{\text{number of doublings}}
\]
Substituting in the values we have:
\[
\text{Final population} = 10,710 \times 2^4
\]
3. **Calculate \(2^4\):**
\[
2^4 = 16
\]
4. **Now calculate the final population:**
\[
\text{Final population} = 10,710 \times 16 = 171,360
\]
Therefore, after 516 minutes, there will be **171,360 bacteria** in the colony.
1. **Calculate the number of doubling periods:**
\[
\text{Number of doubling periods} = \frac{\text{Total time}}{\text{Time per doubling}} = \frac{516 \text{ minutes}}{129 \text{ minutes}} \approx 4
\]
2. **Determine the number of bacteria after 4 doublings:**
Since the colony doubles in size with each period, we can use the formula:
\[
\text{Final population} = \text{Initial population} \times 2^{\text{number of doublings}}
\]
Substituting in the values we have:
\[
\text{Final population} = 10,710 \times 2^4
\]
3. **Calculate \(2^4\):**
\[
2^4 = 16
\]
4. **Now calculate the final population:**
\[
\text{Final population} = 10,710 \times 16 = 171,360
\]
Therefore, after 516 minutes, there will be **171,360 bacteria** in the colony.