Question
If the number of bacteria in a colony doubles every 384 hours and there is currently a population of 2,150 bacteria, what will the population be 1,152 hours from now?
bacteria
bacteria
Answers
GPT-4o mini
To determine the population of the bacteria colony after 1,152 hours, we first need to find out how many times the population doubles in that time period.
1. **Find the number of doubling periods in 1,152 hours**:
Since the bacteria double every 384 hours:
\[
\text{Number of doubling periods} = \frac{1,152 \text{ hours}}{384 \text{ hours/doubling}} = 3
\]
2. **Calculate the population after 3 doublings**:
Starting with a population of 2,150 bacteria, after \( n \) doublings, the population can be calculated using the formula:
\[
\text{Population} = \text{Initial population} \times 2^n
\]
where \( n \) is the number of doublings.
For 3 doublings, we have:
\[
\text{Population} = 2,150 \times 2^3
\]
\[
2^3 = 8
\]
Therefore:
\[
\text{Population} = 2,150 \times 8 = 17,200
\]
So, the population of the bacteria colony after 1,152 hours will be **17,200 bacteria**.
1. **Find the number of doubling periods in 1,152 hours**:
Since the bacteria double every 384 hours:
\[
\text{Number of doubling periods} = \frac{1,152 \text{ hours}}{384 \text{ hours/doubling}} = 3
\]
2. **Calculate the population after 3 doublings**:
Starting with a population of 2,150 bacteria, after \( n \) doublings, the population can be calculated using the formula:
\[
\text{Population} = \text{Initial population} \times 2^n
\]
where \( n \) is the number of doublings.
For 3 doublings, we have:
\[
\text{Population} = 2,150 \times 2^3
\]
\[
2^3 = 8
\]
Therefore:
\[
\text{Population} = 2,150 \times 8 = 17,200
\]
So, the population of the bacteria colony after 1,152 hours will be **17,200 bacteria**.