Calculating Total Number of Live Viruses after 10 Seconds

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The discussion revolves around calculating the total number of live viruses after 10 seconds, given that each virus produces two new viruses every second and has a lifespan of five seconds. The initial confusion stems from miscalculating the number of dead viruses and their impact on reproduction. It is clarified that dead viruses do not contribute to new births, leading to a reevaluation of the total count at each second. By constructing a table to track the number of live viruses, it becomes evident that the correct total at t=10 is 31, not the initially assumed 35. The participants express gratitude for the clarification, highlighting the importance of considering the lifespan of the viruses in the calculations.
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Homework Statement



A virus give birth to 2 new virus in each second and life span of each virus is 5 seconds.The process of reproduction is continuous until the death of the virus.Initially there is one newly born virus at time t=0.Find the total number of live viruses just after 10 seconds.

Homework Equations



number of viruses born - number of viruses dead

The Attempt at a Solution



Number of born viruses = 1+2+4+8+...+1024
Number of viruses dead = 0x4+(1+2+4+...+64)

there fore, answer = 27+28+29+210

but the given answer is 35(35-1)
Nowhere near!

pls help...
 
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johncena said:

Homework Statement



A virus give birth to 2 new virus in each second and life span of each virus is 5 seconds.The process of reproduction is continuous until the death of the virus.Initially there is one newly born virus at time t=0.Find the total number of live viruses just after 10 seconds.

Homework Equations



number of viruses born - number of viruses dead

The Attempt at a Solution



Number of born viruses = 1+2+4+8+...+1024
Number of viruses dead = 0x4+(1+2+4+...+64)

there fore, answer = 27+28+29+210

but the given answer is 35(35-1)
Nowhere near!

pls help...

3^5*(3^5-1)=58806. Even if no viruses die, that's way to big be the answer after 10 seconds. If that's the given answer, there is something wrong with it. But your answer isn't right either. Dead viruses don't reproduce.
 
Sir, i can't get you ... can you explain a bit more?
you mean that no more viruses reproduce after 5 seconds?
 
johncena said:
Sir, i can't get you ... can you explain a bit more?
you mean that no more viruses reproduce after 5 seconds?

I mean that the ones that have died don't contribute to the count of born ones. Try working this out as a table. At t=4 you have 16. At t=5 you have 32, then you remove the old one so you get 31. How many at t=6?
 
Ohhhh...i missed that point...

thanks sir...you was very helpful...
 

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