You brush your teeth very, very carefully in the morning at 6am leaving only 1000 bacteria on your teeth. If this particular bacteria divides every 20 minutes, how many bacteria will you have on your teeth by 8 o'clock that evening? If you have an important date with that "special someone" should you brush your teeth again?
You brush your teeth very, very carefully in the morning at 6am leaving only 1000 bacteria on your teeth. If this particular bacteria divides every 20 minutes, how many bacteria will you have on your teeth by 8 o'clock that evening? If you have an important date with that "special someone" should you brush your teeth again?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Question 6:**
You brush your teeth very, very carefully in the morning at 6am leaving only 1000 bacteria on your teeth. If this particular bacteria divides every 20 minutes, how many bacteria will you have on your teeth by 8 o’clock that evening? If you have an important date with that “special someone” should you brush your teeth again?
**Explanation:**
To determine the number of bacteria present at 8 o'clock in the evening, we need to calculate the bacterial growth over the time period from 6am to 8pm.
1. Calculate the total time in minutes between 6am and 8pm:
- From 6am to 8pm is 14 hours.
- 14 hours * 60 minutes/hour = 840 minutes
2. Determine the number of 20-minute intervals in 840 minutes:
- 840 minutes / 20 minutes/interval = 42 intervals
3. Use the formula for bacterial growth, which is exponential. If a bacteria divides every 20 minutes, after each interval, the number of bacteria doubles. So, after 42 intervals, the number of bacteria can be calculated as:
\[
\text{Number of bacteria} = 1000 \times 2^{42}
\]
Calculating \( 2^{42} \):
\[
2^{42} = 4,398,046,511,104
\]
4. Therefore, the number of bacteria after 42 intervals:
\[
1000 \times 4,398,046,511,104 = 4.398 \times 10^{15} \text{ bacteria}
\]
So, by 8pm, the number of bacteria on your teeth would be approximately 4.398 × 10^{15}.
**Conclusion:**
Yes, it's highly advisable to brush your teeth again before your important date with that "special someone" to maintain good oral hygiene and fresh breath.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80b1b221-3b74-460d-9079-f2de5ffa7b08%2F4def1311-d616-4f60-909a-7223a2888f06%2Fek60bpm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 6:**
You brush your teeth very, very carefully in the morning at 6am leaving only 1000 bacteria on your teeth. If this particular bacteria divides every 20 minutes, how many bacteria will you have on your teeth by 8 o’clock that evening? If you have an important date with that “special someone” should you brush your teeth again?
**Explanation:**
To determine the number of bacteria present at 8 o'clock in the evening, we need to calculate the bacterial growth over the time period from 6am to 8pm.
1. Calculate the total time in minutes between 6am and 8pm:
- From 6am to 8pm is 14 hours.
- 14 hours * 60 minutes/hour = 840 minutes
2. Determine the number of 20-minute intervals in 840 minutes:
- 840 minutes / 20 minutes/interval = 42 intervals
3. Use the formula for bacterial growth, which is exponential. If a bacteria divides every 20 minutes, after each interval, the number of bacteria doubles. So, after 42 intervals, the number of bacteria can be calculated as:
\[
\text{Number of bacteria} = 1000 \times 2^{42}
\]
Calculating \( 2^{42} \):
\[
2^{42} = 4,398,046,511,104
\]
4. Therefore, the number of bacteria after 42 intervals:
\[
1000 \times 4,398,046,511,104 = 4.398 \times 10^{15} \text{ bacteria}
\]
So, by 8pm, the number of bacteria on your teeth would be approximately 4.398 × 10^{15}.
**Conclusion:**
Yes, it's highly advisable to brush your teeth again before your important date with that "special someone" to maintain good oral hygiene and fresh breath.
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