Every hour the number of bacteria in a sample doubles. If the original number of bacteria is 100, and 50 bacteria are removed every two hours, after five hours, there are
Understanding the Bacteria Growth and Removal Problem
This problem involves calculating the number of bacteria in a sample over time, considering both exponential growth (doubling every hour) and periodic removal.
We start with an initial number of bacteria and track how the count changes hour by hour for a duration of five hours, accounting for the doubling and the removal of 50 bacteria every two hours.
Step-by-Step Calculation of Bacteria Count
Let's track the number of bacteria hour by hour, starting from the initial number and applying the rules:
- Initial Count: 100 bacteria.
- Growth Rule: The number of bacteria doubles every hour.
- Removal Rule: 50 bacteria are removed every two hours (at the end of hour 2, hour 4, etc.).
We can represent the change over five hours in a table:
| Time (Hours) | Event | Calculation | Bacteria Count |
|---|---|---|---|
| 0 | Start | 100 | |
| 1 | Doubles | $100 \times 2$ | 200 |
| 2 | Doubles, then Remove 50 | $(200 \times 2) - 50 = 400 - 50$ | 350 |
| 3 | Doubles | $350 \times 2$ | 700 |
| 4 | Doubles, then Remove 50 | $(700 \times 2) - 50 = 1400 - 50$ | 1350 |
| 5 | Doubles | $1350 \times 2$ | 2700 |
Looking at the table, we can see the number of bacteria at the end of each hour:
- At the start (Time 0): 100 bacteria.
- After 1 hour: $100 \times 2 = 200$ bacteria. No removal yet.
- After 2 hours: The count doubles ($200 \times 2 = 400$), then 50 are removed ($400 - 50 = 350$ bacteria). This is the first removal point.
- After 3 hours: The count doubles ($350 \times 2 = 700$ bacteria). No removal.
- After 4 hours: The count doubles ($700 \times 2 = 1400$), then 50 are removed ($1400 - 50 = 1350$ bacteria). This is the second removal point.
- After 5 hours: The count doubles ($1350 \times 2 = 2700$ bacteria). The next removal point would be at hour 6.
Final Bacteria Count After Five Hours
Following the calculations hour by hour, we find that after five hours, the number of bacteria in the sample is 2700.
Revision Table: Bacteria Problem Key Points
| Aspect | Description |
|---|---|
| Initial Bacteria | 100 |
| Growth Rate | Doubles every hour ($\times 2$) |
| Removal Amount | 50 bacteria |
| Removal Frequency | Every two hours (at end of hour 2, 4, 6, ...) |
| Duration | 5 hours |
Additional Information: Exponential Growth and Population Dynamics
This bacteria problem is a simple example of population dynamics where growth and decay/removal processes occur simultaneously. The doubling of bacteria every hour represents exponential growth, a common model for populations with unlimited resources.
Exponential growth can be described by the formula $P(t) = P_0 \times r^t$, where:
- $P(t)$ is the population at time $t$.
- $P_0$ is the initial population.
- $r$ is the growth factor per unit of time (in this case, $r=2$ for doubling every hour).
- $t$ is the time elapsed.
In this specific problem, the removal of bacteria complicates the simple exponential model, requiring a step-by-step calculation to account for the periodic reduction in population.
Important Questions from Environmental Education - Teaching
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Environmental education makes individuals aware of environmental issues, explore and analyse causes and effectiveness of the issues, and promotes environmental sustainability.
Reason R: It is very essential to think and act creatively to become technically capable and trained to approach environmental issues in a proactive manner.
In light of the above statements, choose the most appropriate answer from the options given belowHelping individuals and social groups acquire social values, contributes to development of:
The underlying purpose of environmental education is to:
A. Adjust to environmental challenges.
B. Help face environmental hazards.
C. Promote an individual's critical thinking about emerging issues.
D. Increase public awareness and knowledge of environmental issues.
E. Enhance problem-solving and decision-making skills in respect of handling environmental issues.
Choose the correct answer from the options given below:
Given below are two statements:
Statement I: All potential pollutants are synthetic chemicals.
Statement II: Many of the emerging contaminants have been observed to bioaccumulate in wildlife and humans.
In the light of the above statements, choose the correct answer from the options given below:
Environmental education must be integral to all academic programmes as students need to be mainly sensitized about
