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A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at time t = 0, the find the total number of live bacteria just after 10 seconds :
- a)310 /2
- b)310 - 210
- c)243 *(35 -1)
- d)310 -25
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A bacteria gives birth to two new bacteria in each second and the life...
Total number of bacteria after 10 seconds,
= 3^10 - 3^5
= 3^5 *(3^5 -1)
= 243 *(3^5 -1)
Since, just after 10 seconds all the bacterias (i.e. 3^5 ) are dead after living 5 seconds each.
Most Upvoted Answer
A bacteria gives birth to two new bacteria in each second and the life...
At T=0, there was only 1 bacteria
At T= 1, 1 bacteria gives birth to 2 bacteria so total bacteria become 3
At T=2, each 3 bacteria gives birth to 2 more bacteria... so total bacteria 3*2+3=9 or we can wright it as 3²
At T=3, 3³
At T=4, 3⁴
At T=10, 3¹⁰
Since bacteria die after 5 sec so all the bacteria born from T=0 to T=5 will die at T=10
therefore
3¹⁰-3⁵
3⁵(3⁵-1)
243*(3⁵-1) answer
At T= 1, 1 bacteria gives birth to 2 bacteria so total bacteria become 3
At T=2, each 3 bacteria gives birth to 2 more bacteria... so total bacteria 3*2+3=9 or we can wright it as 3²
At T=3, 3³
At T=4, 3⁴
At T=10, 3¹⁰
Since bacteria die after 5 sec so all the bacteria born from T=0 to T=5 will die at T=10
therefore
3¹⁰-3⁵
3⁵(3⁵-1)
243*(3⁵-1) answer
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Community Answer
A bacteria gives birth to two new bacteria in each second and the life...
Problem Statement: A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. Initially, there is one newly born bacteria at time t=0, then find the total number of live bacteria just after 10 seconds.
Solution:
Given,
- Each bacteria gives birth to two new bacteria in each second, so the number of bacteria doubles every second.
- The life span of each bacteria is 5 seconds.
- Initially, there is one newly born bacteria at time t=0.
To solve this problem, we can calculate the number of live bacteria after each second until 10 seconds and add them up to get the total number of live bacteria just after 10 seconds.
Let's calculate the number of live bacteria after each second:
- At t=0, there is one newly born bacteria. So, the total number of live bacteria at t=0 is 1.
- At t=1, the one bacteria gives birth to two new bacteria. So, the total number of live bacteria at t=1 is 1*2=2.
- At t=2, each of the two bacteria gives birth to two new bacteria. So, the total number of live bacteria at t=2 is 2*2=4.
- At t=3, each of the four bacteria gives birth to two new bacteria. So, the total number of live bacteria at t=3 is 4*2=8.
- At t=4, each of the eight bacteria gives birth to two new bacteria. So, the total number of live bacteria at t=4 is 8*2=16.
- At t=5, each of the sixteen bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the initial bacteria that was born at t=0 dies now. So, the total number of live bacteria at t=5 is 16*2-1=31.
- At t=6, each of the thirty-one bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the bacteria that were born at t=1 also dies now. So, the total number of live bacteria at t=6 is 31*2-2=60.
- At t=7, each of the sixty bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the bacteria that were born at t=2 also dies now. So, the total number of live bacteria at t=7 is 60*2-4=116.
- At t=8, each of the one hundred and sixteen bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the bacteria that were born at t=3 also dies now. So, the total number of live bacteria at t=8 is 116*2-8=224.
- At t=9, each of the two hundred and twenty-four bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the bacteria that were born at t=4 also dies now. So, the total number of live bacteria at t=9 is 224*2-16=432.
- At t
Solution:
Given,
- Each bacteria gives birth to two new bacteria in each second, so the number of bacteria doubles every second.
- The life span of each bacteria is 5 seconds.
- Initially, there is one newly born bacteria at time t=0.
To solve this problem, we can calculate the number of live bacteria after each second until 10 seconds and add them up to get the total number of live bacteria just after 10 seconds.
Let's calculate the number of live bacteria after each second:
- At t=0, there is one newly born bacteria. So, the total number of live bacteria at t=0 is 1.
- At t=1, the one bacteria gives birth to two new bacteria. So, the total number of live bacteria at t=1 is 1*2=2.
- At t=2, each of the two bacteria gives birth to two new bacteria. So, the total number of live bacteria at t=2 is 2*2=4.
- At t=3, each of the four bacteria gives birth to two new bacteria. So, the total number of live bacteria at t=3 is 4*2=8.
- At t=4, each of the eight bacteria gives birth to two new bacteria. So, the total number of live bacteria at t=4 is 8*2=16.
- At t=5, each of the sixteen bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the initial bacteria that was born at t=0 dies now. So, the total number of live bacteria at t=5 is 16*2-1=31.
- At t=6, each of the thirty-one bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the bacteria that were born at t=1 also dies now. So, the total number of live bacteria at t=6 is 31*2-2=60.
- At t=7, each of the sixty bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the bacteria that were born at t=2 also dies now. So, the total number of live bacteria at t=7 is 60*2-4=116.
- At t=8, each of the one hundred and sixteen bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the bacteria that were born at t=3 also dies now. So, the total number of live bacteria at t=8 is 116*2-8=224.
- At t=9, each of the two hundred and twenty-four bacteria gives birth to two new bacteria. But, since the life span of each bacteria is 5 seconds, the bacteria that were born at t=4 also dies now. So, the total number of live bacteria at t=9 is 224*2-16=432.
- At t
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A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at timet = 0, the find the total number of live bacteria just after 10 seconds :a)310/2b)310- 210c)243 *(35-1)d)310-25e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at timet = 0, the find the total number of live bacteria just after 10 seconds :a)310/2b)310- 210c)243 *(35-1)d)310-25e)None of theseCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at timet = 0, the find the total number of live bacteria just after 10 seconds :a)310/2b)310- 210c)243 *(35-1)d)310-25e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at timet = 0, the find the total number of live bacteria just after 10 seconds :a)310/2b)310- 210c)243 *(35-1)d)310-25e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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