Question
A colony of 10,710 bacteria doubles in size every 129 minutes. What will the population be 516 minutes from now?
bacteria
bacteria
Answers
GPT-4o mini
To determine the population of bacteria after 516 minutes, we first need to find out how many times the bacteria will double in that period.
1. **Calculate the number of doubling periods:**
\[
\text{Number of doublings} = \frac{\text{Total time}}{\text{Doubling time}} = \frac{516 \text{ minutes}}{129 \text{ minutes}} = 4
\]
2. **Calculate the population after the doublings:**
Since the population doubles every 129 minutes, after 4 doublings, the population will be:
\[
\text{Final population} = \text{Initial population} \times 2^{\text{Number of doublings}} = 10,710 \times 2^4
\]
Now we calculate \(2^4\):
\[
2^4 = 16
\]
3. **Multiply the initial population by 16:**
\[
\text{Final population} = 10,710 \times 16
\]
\[
\text{Final population} = 171,360
\]
Thus, the population of the bacteria after 516 minutes will be **171,360** bacteria.
1. **Calculate the number of doubling periods:**
\[
\text{Number of doublings} = \frac{\text{Total time}}{\text{Doubling time}} = \frac{516 \text{ minutes}}{129 \text{ minutes}} = 4
\]
2. **Calculate the population after the doublings:**
Since the population doubles every 129 minutes, after 4 doublings, the population will be:
\[
\text{Final population} = \text{Initial population} \times 2^{\text{Number of doublings}} = 10,710 \times 2^4
\]
Now we calculate \(2^4\):
\[
2^4 = 16
\]
3. **Multiply the initial population by 16:**
\[
\text{Final population} = 10,710 \times 16
\]
\[
\text{Final population} = 171,360
\]
Thus, the population of the bacteria after 516 minutes will be **171,360** bacteria.